Question

In the given figure, O is centre of circle, ∠QPR = 70° and m(arc PYR) = 160°, then find the value of the following ∠PQR.

Answer 1

Given, ∠QPR = 70°

m(arc PYR) = 160°

∠ = `1/2` m(arc PYR)

Now, m(arc QXR)

∠QPR = `1/2` m (arc QXR)

70° = `1/2` m(arc QXR)

∴ m(arc QXR) = 140°

Now, ∠QOR

using the properties of triangle, we have,

∠QOR = 2∠QPR

= 2 × 70°

= 140°

Now, ∠PQR = `1/2` m(arc PYR)   .....[Inscribed angle theorem]

∠PQR = `1/2 xx 160^circ`

∠PQR = 80°