In triangle ABC, angle C is 77 AD bisector of angle A, angle BAC is 23. Find the degree measure of angle BDA

The bisector of an angle is a ray starting at the apex of the angle that divides the angle into two equal parts.

The bisector AD divides the ΔABC triangle into two triangles ΔABD and ΔADC.

Consider a triangle ΔADC.

Since the bisector divides the angle in half, then:

∠DАС = ∠ВАС / 2;

∠DАС = 23º / 2 = 11.5º.

Since the sum of all the angles of the triangle is 180º, then:

∠ADC = 180º – 77º – 11.5º = 91.5º.

The angle ∠ВDC is a flat angle and is equal to 180º, therefore:

∠ВDA = 180º – АСС;

∠ВDA = 180º – 91.5º = 88.5º.

Answer: the degree measure ∠ВDA is equal to 88.5º.