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∠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