Question

In the given figure, ∠POQ = 100° and ∠PQR° = 30°, then find ∠RPO

Answer 1

∠PRQ = `1/2 ∠"POQ"` ...(Angles at the circumference)

= `1/2 xx 100^circ`

= 50°

∠OPQ + ∠OQP = 180° – 100° ...(Total angles of A is 180°)

= 80°

∴ ∠OPQ = `80/2`

= 40°  ...(Since OP = OQ, radius of the circle)

∠RPQ = 180° − (30 + 50)°

= 100°

∴ ∠RPO = ∠RPQ – ∠OPQ

= 100° – 40°

= 60°