Angles ABC and CBD are adjacent, beam BM is the bisector of angle ABC, angle ABM is 2 times

| May 5, 2021 | education

Angles ABC and CBD are adjacent, beam BM is the bisector of angle ABC, angle ABM is 2 times greater than angle CBD. Find the angles ABC and CBD.

By the condition of the problem, it is specified that the angles ABC and CBD are adjacent, which means that their sum is 180 degrees. The BM beam is the bisector of the ABC angle, which means that the angle is divided in half. The ABM angle is 2 times the CBD angle. Since the value of any angle is not specified, we will designate the CBD angle as x, then the ABM angle will be 2x. The ABM angle is equal to the MBC angle, which means that the MBC is also 2x. Let’s make the equation:

x + 2x + 2x = 180;

5x = 180;

x = 180: 5;

x = 36 (degrees) – angle СBD;

Then the MBC angle will also be equal to 36 * 2 = 72 degrees, and the ABM angle will also be 36 * 2 = 72 degrees. ABC = ABM + MBS = 72 + 72 = 144 degrees.

Answer: 144 degrees and 36 degrees.



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