In Fig. 2, $XAY$ is a tangent to the circle centered at $O$. If $\angle ABO = 40°$, then find $m\angle BAY$ and $m\angle AOB$.

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Question

In Fig. 2, $XAY$ is a tangent to the circle centered at $O$. If $\angle ABO = 40°$, then find $m\angle BAY$ and $m\angle AOB$.

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Accepted Answer

Step 1: $OA = OB \Rightarrow \angle OAB = 40°$
Step 2: $OA \perp AY \Rightarrow \angle BAY = 50°$
Step 3: $\angle AOB = 180° - 80° = 100°$

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