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

| September 30, 2021 | education

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.



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