In the given figure, AT is tangent to a circle centred at O . If $\angle \mathrm{CAT}=40^{\circ}$, then $\angle \mathrm{CBA}$ is equal to
Explanation
Since AT is a tangent to the circle, angle OAT = 90 degrees. Also, angle CAT = 40 degrees. Therefore, angle OCA = 90 - 40 = 50 degrees. Since angle OCA and angle OCB are alternate angles, they are equal. So, angle OCB = 50 degrees. In triangle OBC, angle OBC = 180 - (angle OCB + angle OCB) = 180 - (50 + 50) = 80 degrees. Since angle OBC and angle CBA are alternate angles, they are equal. So, angle CBA = 80 - 40 = 40 + 40 = 80 - 40 = 40 + 30 = 70 degrees.
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