In the triangle ABC, bisectors are drawn from the vertices A and B. The point of their intersection

In the triangle ABC, bisectors are drawn from the vertices A and B. The point of their intersection is indicated by D. Find the angle ADB, if the angle A is 50◦, the angle C is 30◦.

So, we all know that the sum of all the angles of a triangle is 180 °. First of all, let’s find out what the angle B is equal to, if we know that the angle A is 50 °, the angle C is 30 °, and the sum of all three is 180 °, then we get the following equality: B = 180 – 30 – 50 = 100.

The bisector divides angle B in half, that is, 100: 2 = 50.

The bisector also divides the angle A, that is, 50: 2 = 25.

It turns out that the angle ADB = 180 – 50 – 25 = 105.

Answer: 105 °.