Question

In the given Fig. 4.39, ZA = 64°, ZABC = 58°. If BO and CO
are the bisectors of ZABC and ZACB respectively of AABC,
find x° and yº

Answer 1

Hello there,

In ∆ABC,

∠A + ∠B + ∠C = 180°

(all angles in a ∆ add up to 180°)

⇒ 64° + 58° + ∠C = 180°

⇒ 122°+ ∠C = 180°

⇒ ∠C = 180°- 122°

⇒ ∠C = 180°- 122°

⇒ ∠C = 58°

Also we are given that : BO and CO are the bisectors of ∠ABC and ∠ACB respectively.

y = 58/2 = 29°

(since OC is the bisector of ∠C)

thus, y = 29°

now,

in ∆OBC,

∠OCB = 58/2 = 29°

(since OC is the bisector of ∠C)

now,

by angle sum property:

∠OCB + ∠OBC + ∠BOC = 180°

⇒ ∠BOC = 180° - (∠OCB + ∠OBC)

⇒ ∠BOC = 180° - (29° + 29°)

⇒ ∠BOC = 180° - 58° = 122°

in the figure we can see that ∠BOC = x°

therefore x° = 122°

FINAL ANSWER -

x = 122°

y = 29°

HOPE THIS HELPS

THANKS