In triangle ABC, angle C is 25, AD is the bisector of angle A, angle ADB is 80. Find angle B.

To successfully solve this problem, you must clearly remember that the sum of the angles in any triangle is 180 °. Let us take the value of the angles BAD and DAC = x. Consider triangles BAD and ABC and write down the sum of their angles:

1). x + B + 80 = 180 or x + B = 100;

2). 2x + B + 25 = 180 or 2x + B = 155;

We multiply all the terms of equation 1) by 2, we get:

3). 2x + 2B = 200;

Let us subtract from equation 3) equation 2):

(2x + 2B) – (2x + B) = 200 – 155;

Let’s make simple calculations and get:

B = 200 – 155 = 45 °.