ACT Math : How to find an angle in a trapezoid

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #1 : How To Find An Angle In A Trapezoid

Find the measure of angle  in the isosceles trapezoid pictured below.

Screen_shot_2013-03-18_at_3.32.40_pm

 

Possible Answers:

Correct answer:

Explanation:

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°.

Example Question #2 : How To Find An Angle In A Trapezoid

Trapezoid  is an isosceles trapezoid with angle . If  and   are paired, what is the measure of ?

Possible Answers:

Correct answer:

Explanation:

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 .

Example Question #3 : How To Find An Angle In A Trapezoid

Q2

In the isosceles trapezoid above, 

 .  and .

In degrees, what is the measure of  ?

Possible Answers:

Correct answer:

Explanation:

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 :

Example Question #1 : Trapezoids

Given the following isosceles triangle:

Q1

In degrees, find the measure of the sum of  and   in the figure above. 

Possible Answers:

Correct answer:

Explanation:

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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