Question

1. In an isosceles triangle ABC, bisectors of B and C meet at a point O. If A=40°, then BOC=?
(a) 150°
(b) 130°
(c) 70°
d) 110°
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Answer 1

Answer:

d) 110॰

Step-by-step explanation:

In Δ ABC,

AB = BC

⇒ angle ABC = angle ACB (Isosceles Triangle Property)

Let ABC and ACB = x

So, 2x + 40॰ = 180॰ (ASP of Δ)

⇒ 2x = 140

⇒ x = 70॰

Since OB and OC are bisectors of angles ABC and ACB,

Angle OBC = OCB = 35॰

In ΔOBC,

35 + 35+ BOC = 180॰ (ASP of Δ)

⇒ 70 + BOC = 180

⇒ BOC = 110॰