Question

in the given angle A=64°, angle=58°,if bo and co are the bisectors of angle ABC and Angle ACb

Answer 1

This question is incomplete.

The complete question is:

" In the given angle A=64°, angle=58°,if BO and CO are the bisectors of angle ABC and Angle ACB. Find the measure of angle AOB.

Refer to the attached image.

Solution:

Since the bisectors bisects the angle in two equal halves.

Since BO is the bisector of angle ABC

So, $\angle ABO= \frac{1}{2}(58^{\circ})=29^{\circ}$

Since OA is the bisector of angle BAC

So, $\angle OAB= \frac{1}{2}(64^{\circ})=32^{\circ}$

Now, consider triangle AOB,

By angle sum property of triangle,which states that:

"The sum of all the angles of a triangle is 180 degrees".

$\angle OAB+\angle ABO+\angle AOB=180^{\circ}$

$32^{\circ}+29^{\circ}+\angle AOB=180^{\circ}$

$61^{\circ}+\angle AOB=180^{\circ}$

$\angle AOB=180^{\circ}-61^{\circ}=119^{\circ}$

So, the measure of angle AOB is 119 degrees.