ACDE ~ APQR. mLC = 13°

Question

, mLD = 65"
. What are the measures of
angles P. Q, and R?

Answer 1

To find the measures of angles P, Q, and R, we first need to determine the measures of angles A, B, C, and D.

Given that mL_C = 13° and mL_D = 65°, we know that:
m∠C + m∠D = 180° (because they are supplementary angles)

Solving for ∠C:
13 + 65 = ∠C
78 = ∠C

Now we can determine the measures of angles A and B:
m∠A + m∠C = 180°
m∠A + 78 = 180
m∠A = 102°

And:
m∠B + m∠D = 180°
m∠B + 65 = 180
m∠B = 115°

Now we know the measures of all the angles in quadrilateral ACDE:
∠A = 102°
∠C = 78°
∠D = 65°
∠B = 115°

Since ACDE ~ APQR, the corresponding angles are congruent. Therefore:
∠P = ∠A = 102°
∠Q = ∠C = 78°
∠R = ∠D = 65°

So, the measures of angles P, Q, and R are:
∠P = 102°
∠Q = 78°
∠R = 65°