If tangents PA and PB from a point P to a circle with centre O are inclined to each other at angle of 80°, then ∠BOA is equal to ______.

Given: ∠APB = 80°

Property 1: The tangent at a point on a circle is at right angles to the radius obtained by joining center and the point of tangency.

Property 2: Sum of all angles of a quadrilateral = 360°.

By property 1,

∠PAO = 90°

∠PBO = 90°

By property 2,

∠APB + ∠PAO + ∠PBO + ∠AOB = 360°

⇒ ∠AOB = 360° - ∠APB + ∠PAO + ∠PBO

⇒ ∠AOB = 360° - (80° + 90° + 90°)

⇒ ∠AOB = 360° - 260°

⇒ ∠AOB = 100°