Question

triangle b has the angle measures shown below. 62° 144° triangle b the triangles are similar because they each have only acute angles. the triangles are not similar because one of them has an obtuse angle. the triangles are not similar because an 82° angle is not congruent to a 62° angle. the triangles are similar because they each have angles that measure 36°, 62°, 82°.

Explanation:

Step1: Find the third - angle of Triangle B

The sum of angles in a triangle is 180°. Let the third - angle be $x$. We know one angle is 62° and the exterior angle of 144° corresponds to an interior angle of $180 - 144=36°$. So, $x=180-(62 + 36)=82°$.

Step2: Recall the similarity criterion

Two triangles are similar if their corresponding angles are congruent. If both triangles have angles 36°, 62°, and 82°, they are similar.

Answer:

The triangles are similar because they each have angles that measure 36°, 62°, 82°.