In triangle ABC, angle C is 61 degrees, AD is the bisector of angle A, angle BAD is 40 degrees.

In triangle ABC, angle C is 61 degrees, AD is the bisector of angle A, angle BAD is 40 degrees. Find the degree measure of the BDA angle.

The bisector AD divides angle A into two equal angles:

BAD = DAC = 40 °, find the angle A:

A = 40 ° + 40 °;

A = 80 °;

The angles in a triangle add up to 180 °.

Find angle B:

A + B + C = 180 °;

B = 180 ° – (A + C);

B = 180 ° – (80 ° + 61 °);

B = 39 °.

In the triangle ABD, the angles BAD = 40 °, ABD = 30 ° are known.
find the angle BDA:

BAD + ABD + BDA = 180 °;

BDA = 180 ° – (BAD + ABD);

BDA = 180 ° – (40 ° + 30 °);

BDA = 180 ° – 70 °;

BDA = 110 °.