Question

Triangle CDE ~ triangle PQR m<C = 13° m<D = 65° what are the measures of angles P, Q, and R?

Answer 1

Since the triangles CDE and PQR are similar, the corresponding angles are equal.

m<P = 13° (corresponding to angle C)
m<Q = 65° (corresponding to angle D)

To find the measure of angle R, we need to use the fact that the sum of the angles in a triangle is always 180°.

m<P + m<Q + m<R = 180°

13° + 65° + m<R = 180°
78° + m<R = 180°
m<R = 180° - 78°
m<R = 102°

Therefore, the measures of angles P, Q, and R in triangle PQR are:
m<P = 13°
m<Q = 65°
m<R = 102°