Question

TrianglePQR has two known interior angles of 66° and 100°.

TriangleRST has two known interior angles of 14° and 100°.

What can be determined about whether trianglesPQR and RST are similar?

Responses

A. Similarity cannot be determined from the given information.

B. The triangles are not similar.

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

D. The triangles are similar.

Answer 1

Remember that the sum of the interior angles of a triangle is always 180°. We can take advantage of that fact to find the remaining angle in triangle PQR and triangle RST:
For triangle PQR:
c = 180 - (100 + 66)
o = 180 - 166
o = 14
For triangle RST:
B = 180 - (14 + 100)
8 = 180 - 114
B = 66
Since both triangles have interior angles 100°, 66°, and 14°, we can conclude that the triangles are similar.