The bisectors of the outer corners A and C of triangle ABC meet at point H at an angle of 56. Find the angle B of the triangle.

Consider the triangle CAH and find, The sum of the two angles, A and C:
180 ° – 56 ° = 124 °.
Since AH and CH are the bisectors of the outer angles of the triangle ABC, we multiply the result by 2 and we will know the sum of the outer angles A and C:
124 ° * 2 = 248 °.
Find the sum of the interior angles A and C of this triangle:
360 ° – 248 ° = 112 °.
We find the degree measure of the angle B:
180 ° – 112 ° = 68 °.
Answer: in triangle ABC, angle B is 68 °.