Question

In triangle ABC , bisectors of angle A and angle B intersect at point O . If angle C = 70 degree . find measure of angle AOB​

Answer 1

Answer:

Step-by-step explanation:

70degree

Answer 2

Answer:

Step-by-step explanation:

In ∆ABC,

<C = 70°

We know that,

<A + <B + <C = 180° ...(1)

Putting value of <C in eq. 1

We get,

<A + <B = 110° ...(2)

A.T.Q

We need to find <AOB

BISECTOR OF A & B MEETS AT POINT O

In ∆AOB

<OAB = 1/2 of <A (OA IS BISECTOR OF <A)

SIMILARLY

<OBA = 1/2 of <B (OB IS BISECTOR OF <B)

WE KNOW THAT

IN ∆OAB

<AOB + <OBA + <OAB = 180

<AOB + 1/2 of <B + 1/2 of <A = 180

<AOB + 1/2 ( <B + <A ) = 180

Now putting value of <B + < A from eq (2)

< AOB = 180 - 1/2 X (110)

<AOB = 125°

Consider < = angle

That is <A means angle A