Answer:
∠p, ∠q, and ∠r are all 40°
Step-by-step explanation:
ARQ is a triangle so the sum of the interior angles must equal 180°
48 + 52 = 100
180 - 100 = 80°
This means that the last angle, 2p = 80°
If 2p = 80, then ∠p = 40° (divide by 2)
PQR is also a triangle which means PR is a straight line
The angle next to 2p is going to be 100, because 2p was 80 and angles on a straight line add to 180° (180 - 80 = 100)
∠r = ∠p because they are alternate angles (in the sideways Z shape), 40°
∠q can be found by doing:
180 - (∠PAQ + ∠r)
= 180 - (100 + 40)
= 180 - 140
= 40
