In triangle ABC, angle C is equal to 72 degrees, AD is the bisector of angle A.

In triangle ABC, angle C is equal to 72 degrees, AD is the bisector of angle A. Angle BDA is equal to 106 degrees. Find the angle BAD.

The bisector AD bisects this triangle in two. In one of them, in the ADC triangle, we can find the ADC angle adjacent to the BDA angle, which we know by condition:
Angle ADC = 180 ° – Angle BDA = 180 ° – 106 ° = 74 °.
Now CAD will find the unknown third corner in this triangle:
CAD angle = 180 ° – (C angle + ADC angle) = 180 ° – (72 ° + 74 °) = 180 ° – 146 ° = 34 °.
By the condition AD is the bisector of angle A, it follows that the angle CAD = angle BAD = 34 °.
Answer: The BAD angle is 34 °.