In triangle ABC, AE is the bisector, angle B is 72 degrees, angle CAE is 34 degrees. Find the corner C.

Bissetrix AE divides angle A into two equal parts. Since one of the parts (angle SAE) is 34 °, it means that the entire angle A is equal to: 34 ° * 2 = 68 °.

The sum of the angles in any triangle is 180 °. Since we know the degree measure of the angles A and B, we calculate the degree measure of the angle C:

Angle C = 180 ° – (angle A + angle B) = 180 ° – (72 ° + 68 °) = 180 ° – 140 ° = 40 °.

Answer: angle C is 40 °.