In triangle ABC, bisectors AN and BL are drawn, which intersect at point O

In triangle ABC, bisectors AN and BL are drawn, which intersect at point O, angle AOB = 98, find the outer angle at vertex C.

Let the angle ABC = 2 * X0, and the angle BAC = 2 * Y0.

Since BL and AN are bisectors of the angles, then the angle AOL = X0, the angle BAN = Y0.

In the ABO triangle, the sum of the angles will be:

BAO + ABO + AOB = 180.

Y + X + 98 = 180.

X + Y = 180 – 98 = 82.

Multiply both sides of the equality by 2.

2 * X + 2 * Y = 164.

Angle ABC + BAC = 164.

The external angle BCD is equal to the sum of two internal angles that are not adjacent to it.

Angle BCD = ABC + BAC = 164.

Answer: The outer angle at vertex C is 164.