Question

Triangle ABC is similar to triangle QRS by the AA Similarity Postulate.

Also, m∠A = 32° and m∠S = 102°.

What is m∠B

Answer 1

\[\large \triangle \color{red}{A}\color{magenta}{B} \color{blue}{C}~~\sim~~ \color{red}{Q}\color{magenta}{R} \color{blue}{S}\]

Answer 2

what do you know about angles in similar triangles ?

Answer 3

A= 32
S=102

Answer 4

corresponding angles are congruent when triangles are similar, so can we say \(C = S = 102\) ?

Answer 5

that gives us two known angles in the same triangle :

```
A = 32
C = 102
```

use triangle sum property to find the third angle

Answer 6

\[32 + B + 102 = 180\]

solve \(B\)