Answer: 91 degrees.
Explanation:
The quadrilaterals shown in the image are similar.
This means:
- The shape of the two quadrilaterals are identical.
- The corresponding angle measures of the two quadrilaterals are identical.
- The size of each side is proportionally identical to the corresponding sides of the other quadrilateral.
As the corresponding angle measures are identical, you can see that both m∠s and m∠j are 55 degrees. All other corresponding angles are identical, too, so:
m∠j = m∠s
m∠g = m∠r
m∠h = m∠q
m∠i = m∠p
We are trying to find m∠q, which is equal to m∠h. m∠h is shown to be 91 degrees in the quadrilateral on the left, so this is the correct answer.