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.
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 – ADС;
∠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.