Rhombuses - ACT Math
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The two acute angles in a rhombus add up to 
. What is the measure of one of the obtuse angles in the rhombus?
The two acute angles in a rhombus add up to
The key here is to know that a rhombus has two pairs of congruent angles. In other words, the two acute angles of a rhombus are equal and the two obtuse angles are equal.
In this problem, since the two acute angles add up to 
and they must both be the same amount, each of the acute angles must be 
.
It is also important to know that the four angles of a rhombus add up to 
. If the two acute angles add up to 
, then that means that the two obtuse angles must add up to 
, or 
.
Finally, because the obtuse angles add up to 
and they must be congruent, each of the obtuse angles must be 
.
The key here is to know that a rhombus has two pairs of congruent angles. In other words, the two acute angles of a rhombus are equal and the two obtuse angles are equal.
In this problem, since the two acute angles add up to
It is also important to know that the four angles of a rhombus add up to
Finally, because the obtuse angles add up to
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A rhombus has two interior angles each with a measurement of 
. Find the sum of the remaining two angles.
A rhombus has two interior angles each with a measurement of
To solve this problem, consider that the sum total of the four interior angles in any rhombus must equal 
. Furthermore, a rhombus must have two sets of equivalent opposite interior angles, and a rhombus must have two sets of adjacent interior angles. The adjacent interior angles must be supplementary—meaning they have a sum total of 
.
Since this problem provides the measurement for two of the interior angles, find the sum of those two angles. Then subtract that sum from 
to find the sum of the two remaining interior angles.
The solution is:
Note: this means that each of the two remaining angles must have a measurement of 
.
To solve this problem, consider that the sum total of the four interior angles in any rhombus must equal
Since this problem provides the measurement for two of the interior angles, find the sum of those two angles. Then subtract that sum from
The solution is:
Note: this means that each of the two remaining angles must have a measurement of
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A rhombus has two interior angles each with a measurement of 
. Find the measurement for one of the two remaining angles.
A rhombus has two interior angles each with a measurement of
First, consider that the sum total of the four interior angles in any rhombus must equal 
. Furthermore, a rhombus must have two sets of equivalent opposite interior angles, and a rhombus must have two sets of adjacent interior angles. The adjacent interior angles must be supplementary—meaning they have a sum total of 
.
One way to approach this problem is to realize that each of the remaining two angles must have the same measurement, and that each will be supplementary angles with 
. Find the difference between 
and 
to find the solution.
The correct answer is:
First, consider that the sum total of the four interior angles in any rhombus must equal
One way to approach this problem is to realize that each of the remaining two angles must have the same measurement, and that each will be supplementary angles with
The correct answer is:
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A rhombus has an interior angle with a measurement of 
. Find the measurement for one of the angles that are adjacent to the angle that has a measurement of 
.
A rhombus has an interior angle with a measurement of
A rhombus must have two sets of equivalent opposite interior angles, and a rhombus must have two sets of adjacent interior angles. The adjacent interior angles must be supplementary—meaning they have a sum total of 
.
If a rhombus has an interior angle that has a measurement of 
, the adjacent angle must equal:
A rhombus must have two sets of equivalent opposite interior angles, and a rhombus must have two sets of adjacent interior angles. The adjacent interior angles must be supplementary—meaning they have a sum total of
If a rhombus has an interior angle that has a measurement of
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A rhombus has two opposite interior angles that have a sum of 
. Find the sum of the remaining two angles.
A rhombus has two opposite interior angles that have a sum of
The sum total of the four interior angles in any rhombus must equal 
. Furthermore, a rhombus must have two sets of equivalent opposite interior angles, and a rhombus must have two sets of adjacent interior angles. The adjacent interior angles must be supplementary—meaning they have a sum total of 
.
Since, two of the opposite interior angles in this rhombus have a sum measurement of 
, the sum of the remaining two angles must equal:
To check your answer note:
(meaning the sum of the four interior angles equals 
).
The sum total of the four interior angles in any rhombus must equal
Since, two of the opposite interior angles in this rhombus have a sum measurement of
To check your answer note:
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Using the rhombus shown above, find the measurement for angle 
.
Using the rhombus shown above, find the measurement for angle
A rhombus must have two sets of equivalent opposite interior angles, and a rhombus must have two sets of adjacent interior angles. The adjacent interior angles must be supplementary—meaning they have a sum total of 
.
Since this problem involves supplementary angles, the solution is:
A rhombus must have two sets of equivalent opposite interior angles, and a rhombus must have two sets of adjacent interior angles. The adjacent interior angles must be supplementary—meaning they have a sum total of
Since this problem involves supplementary angles, the solution is:
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A rhombus has two interior angles each with a measurement of 
. Find the measurement for one of the two remaining angles.
A rhombus has two interior angles each with a measurement of
The sum total of the four interior angles in any rhombus must equal 
. Furthermore, a rhombus must have two sets of equivalent opposite interior angles, and a rhombus must have two sets of adjacent interior angles. The adjacent interior angles must be supplementary—meaning they have a sum total of 
.
One way to approach this problem is to realize that each of the remaining two angles must have the same measurement, and that each will be supplementary angles with 
.
Find the difference between 
and 
to find the solution.
The sum total of the four interior angles in any rhombus must equal
One way to approach this problem is to realize that each of the remaining two angles must have the same measurement, and that each will be supplementary angles with
Find the difference between
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A rhombus has two interior angles each with a measurement of 
. Find the sum of the remaining two angles.
A rhombus has two interior angles each with a measurement of
To solve this problem, consider that the sum total of the four interior angles in any rhombus must equal 
. Furthermore, a rhombus must have two sets of equivalent opposite interior angles, and a rhombus must have two sets of adjacent interior angles. The adjacent interior angles must be supplementary—meaning they have a sum total of 
.
Since this problem provides the measurement for two of the interior angles, find the sum of those two angles. Then subtract that sum from 
to find the sum of the two remaining interior angles.
The solution is:
To solve this problem, consider that the sum total of the four interior angles in any rhombus must equal
Since this problem provides the measurement for two of the interior angles, find the sum of those two angles. Then subtract that sum from
The solution is:
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A rhombus has two interior angles each with a measurement of 
. Find the sum of the remaining two angles.
A rhombus has two interior angles each with a measurement of
To solve this problem, consider that the sum total of the four interior angles in any rhombus must equal 
. Furthermore, a rhombus must have two sets of equivalent opposite interior angles, and a rhombus must have two sets of adjacent interior angles. The adjacent interior angles must be supplementary—meaning they have a sum total of 
.
Since this problem provides the measurement for two of the interior angles, find the sum of those two angles. Then subtract that sum from 
to find the sum of the two remaining interior angles.
The solution is:
To solve this problem, consider that the sum total of the four interior angles in any rhombus must equal
Since this problem provides the measurement for two of the interior angles, find the sum of those two angles. Then subtract that sum from
The solution is:
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A rhombus has an interior angle with a measurement of 
. Find the measurement for one of the angles that are adjacent to the angle that has a measurement of 
.
A rhombus has an interior angle with a measurement of
A rhombus must have two sets of equivalent opposite interior angles, and a rhombus must have two sets of adjacent interior angles. The adjacent interior angles must be supplementary—meaning they have a sum total of 
.
Therefore, if a rhombus has an interior angle that has a measurement of 
, then the adjacent angle must equal:
A rhombus must have two sets of equivalent opposite interior angles, and a rhombus must have two sets of adjacent interior angles. The adjacent interior angles must be supplementary—meaning they have a sum total of
Therefore, if a rhombus has an interior angle that has a measurement of
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Using the rhombus shown above, find the measurement for angle .
Using the rhombus shown above, find the measurement for angle
A rhombus must have two sets of equivalent opposite interior angles, and a rhombus must have two sets of adjacent interior angles. The adjacent interior angles must be supplementary—meaning they have a sum total of 
.
Since this problem involves supplementary angles, the solution is:
Check answer by:
A rhombus must have two sets of equivalent opposite interior angles, and a rhombus must have two sets of adjacent interior angles. The adjacent interior angles must be supplementary—meaning they have a sum total of
Since this problem involves supplementary angles, the solution is:
Check answer by:
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A rhombus has two interior angles each with a measurement of 
. Find the measurement for one of the two remaining angles.
A rhombus has two interior angles each with a measurement of
First, consider that the sum total of the four interior angles in any rhombus must equal 
. Secondly, a rhombus must have two sets of equivalent opposite interior angles, and a rhombus must have two sets of adjacent interior angles. The adjacent interior angles must be supplementary—meaning they have a sum total of 
.
One way to approach this problem is to realize that each of the remaining two angles must have the same measurement, and that each will be supplementary angles with 
. Therefore, find the difference between 
and 
to find the solution.
First, consider that the sum total of the four interior angles in any rhombus must equal
One way to approach this problem is to realize that each of the remaining two angles must have the same measurement, and that each will be supplementary angles with
Compare your answer with the correct one above
A rhombus has two interior angles each with a measurement of 
. Find the measurement for one of the two remaining angles.
A rhombus has two interior angles each with a measurement of
A rhombus must have two sets of equivalent opposite interior angles, and a rhombus must have two sets of adjacent interior angles. The adjacent interior angles must be supplementary—meaning they have a sum total of 
.
One way to approach this problem is to realize that each of the remaining two angles must have the same measurement, and that each will be supplementary angles with 
. Find the difference between 
and 
to find the solution.
A rhombus must have two sets of equivalent opposite interior angles, and a rhombus must have two sets of adjacent interior angles. The adjacent interior angles must be supplementary—meaning they have a sum total of
One way to approach this problem is to realize that each of the remaining two angles must have the same measurement, and that each will be supplementary angles with
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A quadrilateral ABCD has diagonals that are perpendicular bisectors of one another. Which of the following classifications must apply to quadrilateral ABCD?
I. parallelogram
II. rhombus
III. square
A quadrilateral ABCD has diagonals that are perpendicular bisectors of one another. Which of the following classifications must apply to quadrilateral ABCD?
I. parallelogram
II. rhombus
III. square
If the diagonals of a quadrilateral are perpendicular bisectors of one another, then the quadrilateral must be a rhombus, but not necessarily a square. Since all rhombi are also parallelograms, quadrilateral ABCD must be both a rhombus and parallelogram.
If the diagonals of a quadrilateral are perpendicular bisectors of one another, then the quadrilateral must be a rhombus, but not necessarily a square. Since all rhombi are also parallelograms, quadrilateral ABCD must be both a rhombus and parallelogram.
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Are the two rhombuses in the above picture similar?
Are the two rhombuses in the above picture similar?
Two shapes are similar to each other if they are the same except for differences in scaling. This means that all of the angles of one shape have to be the same as the angles of the other shape, and all the sides have to be proportional to each other. For example, if we have two rectangles A and B, where A has side lengths 2 and 4, and B has side lengths 5 and 10, A and B are similar because the ratio between 2 and 4 is the same as the ratio between 5 and 10, and also the ratio between 2 and 5 is the same as the ratio between 4 and 10. Everything is proportional (and all the angles are the same) so the two rectangles A and B are similar.
The two rhombuses in our figure are not similar to each other, because we can see the larger angle in the rhombus on the left is not the same as the larger angle in the rhombus on the right. If we scaled the larger rhombus down and tried to cover up the smaller rhombus with it, it wouldn't work because they aren't proportional to each other.
Two shapes are similar to each other if they are the same except for differences in scaling. This means that all of the angles of one shape have to be the same as the angles of the other shape, and all the sides have to be proportional to each other. For example, if we have two rectangles A and B, where A has side lengths 2 and 4, and B has side lengths 5 and 10, A and B are similar because the ratio between 2 and 4 is the same as the ratio between 5 and 10, and also the ratio between 2 and 5 is the same as the ratio between 4 and 10. Everything is proportional (and all the angles are the same) so the two rectangles A and B are similar.
The two rhombuses in our figure are not similar to each other, because we can see the larger angle in the rhombus on the left is not the same as the larger angle in the rhombus on the right. If we scaled the larger rhombus down and tried to cover up the smaller rhombus with it, it wouldn't work because they aren't proportional to each other.
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A rhombus contains diagonals with the length 
and 
. Find the area of the rhombus.
A rhombus contains diagonals with the length
The equation for the area of a rhombus is given by:
where 
and 
are the two diagonal lengths.
This problem very quickly becomes one of the "plug and chug" type, where the given values just need to be substituted into the equation and the equation then solved. By plugging in the values given, we get:
The equation for the area of a rhombus is given by:
where
This problem very quickly becomes one of the "plug and chug" type, where the given values just need to be substituted into the equation and the equation then solved. By plugging in the values given, we get:
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Find the area of a rhombus if the diagonals lengths are 
and 
.
Find the area of a rhombus if the diagonals lengths are
Write the formula for the area of a rhombus:
Substitute the given lengths of the diagonals and solve:
Write the formula for the area of a rhombus:
Substitute the given lengths of the diagonals and solve:
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Find the area of a rhombus if the diagonals lengths are 
and 
.
Find the area of a rhombus if the diagonals lengths are
Write the formula for finding the area of a rhombus. Substitute the diagonals and evaluate.
Write the formula for finding the area of a rhombus. Substitute the diagonals and evaluate.
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If the area of a rhombus is 
, and the length of one of its diagonals is 
, what must be the length of the other diagonal?
If the area of a rhombus is
Write the formula for the area of a rhombus.
Plug in the given area and diagonal length. Solve for the other diagonal.
Write the formula for the area of a rhombus.
Plug in the given area and diagonal length. Solve for the other diagonal.
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If the diagonals of a rhombus were 
and 
, what is the side length of the rhombus?
If the diagonals of a rhombus were
Write the formula used to find the rhombus side length given 2 diagonals.
Substitute both diagonals in the equation and simplify.
Write the formula used to find the rhombus side length given 2 diagonals.
Substitute both diagonals in the equation and simplify.
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