In the given figure, PA and PB are tangents to a circle with centre O. If $∠ A P B = {(2 x + 3)}^{0} a n d ∠ A O B = {(3 x + 7)}^{0},$ then find the value of x.

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Solution

$∠ A P B = (2 x + 3)$
$∠ A O B = (3 x + 7)$
$2 x + 3 + 3 x + 7 = 180^{\circ}$
$5 x + 10 = 180^{\circ} \Rightarrow 5 x = 170$
$x = 34^{\circ}$

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