ACDE ~ APQR. m<C = 13°

Question

,mLD = 65°
. What are the measures of angles P, Q, and R? (2 points)
mLP = ]°. m<Q = L
and mLR =
200

Answer 1

Given the Diagram:

A----C----D----E
|
|
L----D

We can see that:

m<C = m<Q because alternate interior angles are equal.
mLD = mLR because they are corresponding angles.

Therefore, m<Q = 13°.

To find m<P:

mLP + m<C = 180° (because they form a straight line)
mLP + 13° = 180°
mLP = 180° - 13°
mLP = 167°

To find m<R:

mLD + mQR = 180° (because they form a straight line)
65° + mQR = 180°
mQR = 180° - 65°
mQR = 115°

Therefore, the measures of angles P, Q, and R are:

m<P = 167°
m<Q = 13°
m<R = 115°