Question

Triangle PQR has two known interior angles of 24°, and 100°.

Triangle RST has two known interior angles of 24°, and 56°.

 What can be determined about whether triangles PQR and RST are similar?

A. All interior angles must be given to determine similarity.

B. Similarity cannot be determined from the given information.

C. The triangles are not similar.

D. The triangles are similar.

Answer 1

180-24=5
180-56=34
Both are equal
D

Answer 2

D. The triangles are similar.

Explanation:

Two triangles are similar if all 3 angles of one triangle are congruent to all 3 angles of the other triangle.

In triangle PQR, the two known angles are 24° and 100°. Since the sum of the measures of the angles of a triangle is always 180°, this makes the missing angle

180-(24+100) = 180-124 = 56°

In triangle RST, the two known angles are 24° and 56°. This makes the missing angle

180-(24+56) = 180-80 = 100°

This means all 3 angles in PQR are congruent to all 3 angles in RST; this means the triangles are similar.