How to find an angle in a trapezoid - ACT Math
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Find the measure of angle 
in the isosceles trapezoid pictured below.
Find the measure of angle
The sum of the angles in any quadrilateral is 360**°, and the properties of an isosceles trapezoid dictate that the sets of angles adjoined by parallel lines (in this case, the bottom set and top set of angles) are equal. Subtracting 2(72°) from 360°** gives the sum of the two top angles, and dividing the resulting 216**°** by 2 yields the measurement of x, which is 108**°**.
The sum of the angles in any quadrilateral is 360**°, and the properties of an isosceles trapezoid dictate that the sets of angles adjoined by parallel lines (in this case, the bottom set and top set of angles) are equal. Subtracting 2(72°) from 360°** gives the sum of the two top angles, and dividing the resulting 216**°** by 2 yields the measurement of x, which is 108**°**.
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Given the following isosceles triangle:
In degrees, find the measure of the sum of 
and 
in the figure above.
Given the following isosceles triangle:
In degrees, find the measure of the sum of
All quadrilaterals' interior angles sum to 360°. In isosceles trapezoids, the two top angles are equal to each other.
Similarly, the two bottom angles are equal to each other as well.
Therefore, to find the sum of the two bottom angles, we subtract the measures of the top two angles from 360:
All quadrilaterals' interior angles sum to 360°. In isosceles trapezoids, the two top angles are equal to each other.
Similarly, the two bottom angles are equal to each other as well.
Therefore, to find the sum of the two bottom angles, we subtract the measures of the top two angles from 360:
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In the isosceles trapezoid above,
. 
and 
.
In degrees, what is the measure of 
?
In the isosceles trapezoid above,
In degrees, what is the measure of
To find the measure of angle DAC, we must know that the interior angles of all triangles sum up to 180 degrees. Also, as this is an isosceles trapezoid, 
and 
are equal to each other. The two diagonals within the trapezoid bisect angles 
and 
at the same angle.
Thus, 
must also be equal to 50 degrees.
Thus, 
.
Now that we know two angles out of the three in the triangle on the left, we can subtract them from 180 degrees to find 
:
To find the measure of angle DAC, we must know that the interior angles of all triangles sum up to 180 degrees. Also, as this is an isosceles trapezoid,
Thus,
Thus,
Now that we know two angles out of the three in the triangle on the left, we can subtract them from 180 degrees to find
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Trapezoid 
is an isosceles trapezoid with angle 
. If 
and 
are paired, what is the measure of 
?
Trapezoid
As a rule, adjacent (non-paired) angles in a trapezoid are supplementary. Thus, we know that if 
, then 
. Since we are told that 
and 
are paired and trapezoid 
is isosceles, 
must also equal 
.
As a rule, adjacent (non-paired) angles in a trapezoid are supplementary. Thus, we know that if
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