# In triangle ABC, angle C = 45 °, AD bisector, CAD = 30 °. Find Angle B.

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.

Let’s calculate the degree measure of the angle ∠ADC. Since the sum of all the angles of the triangle is 180º, then:

∠ADС = 180º – ∠DСА – ∠DАС;

∠ADC = 180º – 45º – 30º = 105º.

Since the angle ∠ВDC is a deployed angle (equal to 180º), then:

∠ВDA = 180º – 105º = 75º.

Since the bisector of an angle divides it in half, then:

∠ВАD = ∠DАС = 30º.

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

∠АВD = 180º – 30º – 75º = 75º.

Answer: the degree measure of the angle ∠В is equal to 75º. One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.