Question

In the given figure, ∠A = 64°, ∠ABC = 58°. If BO and CO are the bisectors of ∠ABC and ∠ACB respectively of ΔABC, find x° and y°

Answer 1

In the given ΔABC

∠A = 64° and ∠B = 58°

∠C = 180° − (64° + 58°)

= 180° – 122°

= 58°

Since OC is the bisector of ∠C

y = `(58^circ)/2`

= 29°

Given ΔOBC

∠OCB = `(58^circ)/2` = 29°

∠OCB = 29°

∴ ∠BOC = 180° − (29° + 29°)

x = 180° – 58°

x = 122°

∠x = 122° and ∠y = 29°.