Answer:
p = 20, q = 20, r = 30
Step-by-step explanation:
The triangle to the left of OA is isosceles ( 2 equal radii ), then the base angles are congruent, so
p = 20
The 3 angles in this triangle sum to 180°, then the angle at O is
180 - (20 + 20) = 180 - 40 = 140°
AB is a straight line so angle in triangle containing q is 180 - 140 = 40
The triangle containing q is also isosceles ( 2 equal radii ) then base angles are congruent, then
q = [tex]\frac{180-140}{2}[/tex] = [tex]\frac{40}{2}[/tex] = 20
The triangle to the right of OA is also isosceles ( 2 equal radii ) then the base angles are congruent, so
r = 30
Then p = 20, q = 20, r = 30