In triangle ABC, angle C is 50 degrees. Find the angle AOB, where point O is the intersection

In triangle ABC, angle C is 50 degrees. Find the angle AOB, where point O is the intersection point of the bisectors of the triangle.

The sum of the angles of the triangle ABC:

<BAC + <ABC + ACB = 180 °;

<BAC + <ABC + 50 ° = 180 °;

<BAC + <ABC = 130 °;

<BAO = <BAC / 2;

<ABO = ABC / 2;

The sum of the angles for the triangle AOB:

<BAO + <ABO + <AOB = 180 °

<AOB = 180 ° – (<BAO + <ABO) = 180 ° – (<BAC / 2 + ABC / 2) =

= 180 ° – (<BAC + ABC) / 2 = 180 ° – 130 ° / 2 = 180 ° – 65 ° = 115 °.

Answer: 115 °.