Question

P is the circumference of ∆ABC measure of angle ABC is 60⁰ and measure of angle PBC is 55⁰ then find m(arcBXC) and m(arc BAC) ​

Answer 1

Answer:

Answer

AO and OB are radii of the circle.

side AO=BO so, ∠OAB=∠OBA [Isosceles triangle AOB]

Angle subtended by chord at the centre of a circle is double of the angle subtended at it's circumference.

Therefore ∠AOB=2∠ACB

∠AOB=100

∘

In triangle AOB

The sum of all three angle will be 180

∘

So, ∠AOB+∠OBA+∠OAB=180

∘

100

∘

+∠OBA+∠OAB=180

∘

100

∘

+2∠OAB=180

∘

[∠OAB=∠OBA]

∠OAB=

2

80

∘

∠OAB=40

∘

Therefore option B is the answer