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Answer:
r = 80°, s = 80°, t = 10°, u = 60°, v = 30°
Explanation:
Working clockwise from the left side, we can name the points on the circle as A, B, C, D. The given inscribed angles are half the measure of the arcs they intercept, so we have ...
arc BD = 2×40° = 80°
arc DA = 2×60° = 120°
arc CD = 2×10° = 20°
From these measures, we can deduce the measures of the individual arcs as ...
arc AB = 360° -BD -DA = 360° -80° -120° = 160°
arc BC = BD -CD = 80° -20° = 60°
Then the angle measures of interest are ...
r = AB/2 = 80°
s = AB/2 = 80°
t = CD/2 = 10°
u = DA/2 = 60°
v = BC/2 = 30°