ACDE ~ APQR. mLC = 13°
, mLD = 65"
. What are the measures of
angles P. Q, and R?
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°