How to find an angle in a parallelogram - GRE Quantitative Reasoning
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In a given parallelogram, the measure of one of the interior angles is 25 degrees less than another. What is the approximate measure rounded to the nearest degree of the larger angle?
In a given parallelogram, the measure of one of the interior angles is 25 degrees less than another. What is the approximate measure rounded to the nearest degree of the larger angle?
There are two components to solving this geometry puzzle. First, one must be aware that the sum of the measures of the interior angles of a parallelogram is 360 degrees (sum of the interior angles of a figure = 180(n-2), where n is the number of sides of the figure). Second, one must know that the other two interior angles are doubles of those given here. Thus if we assign one interior angle as x and the other as x-25, we find that x + x + (x-25) + (x-25) = 360. Combining like terms leads to the equation 4x-50=360. Solving for x we find that x = 410/4, 102.5, or approximately 103 degrees. Since x is the measure of the larger angle, this is our answer.
There are two components to solving this geometry puzzle. First, one must be aware that the sum of the measures of the interior angles of a parallelogram is 360 degrees (sum of the interior angles of a figure = 180(n-2), where n is the number of sides of the figure). Second, one must know that the other two interior angles are doubles of those given here. Thus if we assign one interior angle as x and the other as x-25, we find that x + x + (x-25) + (x-25) = 360. Combining like terms leads to the equation 4x-50=360. Solving for x we find that x = 410/4, 102.5, or approximately 103 degrees. Since x is the measure of the larger angle, this is our answer.
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Figure 
is a parallelogram.
What is 
in the figure above?
Figure
What is
Because of the character of parallelograms, we know that our figure can be redrawn as follows:
Because it is a four-sided figure, we know that the sum of the angles must be 
. Thus, we know:
Solving for 
, we get:
Because of the character of parallelograms, we know that our figure can be redrawn as follows:
Because it is a four-sided figure, we know that the sum of the angles must be
Solving for
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Figure 
is a parallelogram.
Quantity A: The largest angle of 
.
Quantity B: 
Which of the following is true?
Figure
Quantity A: The largest angle of
Quantity B:
Which of the following is true?
By using the properties of parallelograms along with those of supplementary angles, we can rewrite our figure as follows:
Recall, for example, that angle 
is equal to:
, hence 
Now, you know that these angles can all be added up to 
. You should also know that 
Therefore, you can write:
Simplifying, you get:
Now, this means that:
and 
. Thus, the two values are equal.
By using the properties of parallelograms along with those of supplementary angles, we can rewrite our figure as follows:
Recall, for example, that angle
Now, you know that these angles can all be added up to
Therefore, you can write:
Simplifying, you get:
Now, this means that:
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