Using the tangent theorem and the inscribed angle theorem, the measure of angle YAC in the figure is: 70°.
What is the Tangent Theorem?
The angle formed at the point of tangency of the radius and the tangent equals 90 degrees based on the tangent theorem.
What is the Inscribed Angle Theorem?
According to the inscribed angle theorem, an inscribed angle equals the measure of the arc intercepted.
m∠BAY = 1/2(40) [inscribed angle theorem]
m∠BAY = 20°
m∠BAC = 90° [tangent theorem]
m∠YAC = 90 - 20
m∠YAC = 70°
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