Answer:
∠ 1 = 29° , ∠ 2 = 66° , ∠ 3 = 37°
Step-by-step explanation:
The measure of the secant- secant angle 1 is half the difference of the measures of the intercepted arcs , that is
∠ 1 = [tex]\frac{1}{2}[/tex] (96 - 38)° = [tex]\frac{1}{2}[/tex] × 58° = 29°
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The measure of the chord- chord angle 2 is half the sum of the measures of the arcs intercepted by the angle and its vertical angle, that is
∠ 2 = [tex]\frac{1}{2}[/tex] (96 + 36)° = [tex]\frac{1}{2}[/tex] × 132° = 66°
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The measure of the inscribed angle 3 is half the measure of its intercepted arc, that is
∠ 3 = [tex]\frac{1}{2}[/tex] (36 + 38)° = [tex]\frac{1}{2}[/tex] × 74° = 37°
