In the given figure PA and PB are tangents to a circle with centre O. If ∠APB = (2x³ and ∠AOB = (3x7, then find the value of x)

Question

In the given figure PA and PB are tangents to a circle with centre O. If ∠APB = (2x3 and ∠AOB = (3x7, then find the value of x)

Philoid · Accepted Answer

Now, here, APBO is a quadrilateral where, ∠OAP = 90°& ∠ OBP = 90°

Also, the sum of the angles of the quadrilateral is 360°.

Hence, the sum of opposite angles is 180°.

⇒ ∠AOB + ∠∠APB = 180°

⇒ 3x + 7 + 2x + 3 = 180°

⇒ 5x + 10 = 180

⇒ 5x = 170

⇒ x = 34°