Question

∆RQS is similar to ∆TQU by the AA Similarity Postulate. What is the measure of angle R?

Show all work to verify your conclusion.

Answer 1

`m<R=60\°`

Explanation:

we know that

If two figures are similar, then its corresponding sides are congruent

so

In this problem

m<R=m<T ------> by corresponding angles

Remember that in a triangle the sum of the interior angles must be equal to 180 degrees

`m<Q+m<R+m<S=180\°`

substitute the values

`88\°+m<R+32\°=180\°`

`m<R=180\°-88\°-32\°=60\°`