# In triangle ABC, angle C is 30, AD is the bisector of angle A, angle B is four times greater than ADB

**In triangle ABC, angle C is 30, AD is the bisector of angle A, angle B is four times greater than ADB. Find the degree measure of angle B.**

Let’s introduce the variable x, which will act as the angle ADB, then the angle ABD is equal to 4 * x. Let’s use the rule, which says that the sum of the angles of a triangle is 180, and write down: 180 = DAB + ABD + BDA = DAB + 5 * x.

Since the ADB angle is adjacent to the ADC angle, then ADC = 180 – x.

Now consider the triangle ADC and write a similar equation: 180 = 30 + 180 – x + DAC.

Let’s enter: DАС = 180 – 30 – 180 + x = x – 30

Since AD is the bisector of angle A, we can equate DAC and DAB: x – 30 = 180 – 5 * x.

Let’s solve the equation: 6 * x = 180 + 30; x = 210/6 = 35.

So x = 35, ADB = 35. Then B = 35 * 4 = 140.

Answer: 140.