Question

Луч BM проходит между сторонами угла ABC.Известно что угол ABM в три раза меньше угла MBC.Какова градусная мера угла MBC если угол ABC равен 120 градусам

Answer 1

<ABM=x?<MBC=3x
x+3x=120
4x=120
x=120:4
x=30-<ABM
30*3=90-<MBC

Answer 2

Understanding the problem

Let's break down the problem to better understand it:

- We have a triangle ABC, and there is a point M inside the triangle. - The angle ABM is three times smaller than the angle MBC. - The angle ABC is given as 120 degrees.

We need to find the measure of angle MBC.

Solution

To solve this problem, let's assign variables to the angles we have:

- Let x be the measure of angle ABM. - Let y be the measure of angle MBC.

We know that the measure of angle ABM is three times smaller than the measure of angle MBC. So we can write the equation:

x = (1/3) * y

We also know that the measure of angle ABC is 120 degrees. Since the sum of angles in a triangle is 180 degrees, we can write the equation:

x + y + 120 = 180

Now, we can substitute the value of x from the first equation into the second equation:

(1/3) * y + y + 120 = 180

Simplifying the equation, we can multiply through by 3 to remove the fraction:

y + 3y + 360 = 540

Combining like terms:

4y + 360 = 540

Subtracting 360 from both sides:

4y = 180

Dividing both sides by 4:

y = 45

Therefore, the measure of angle MBC is 45 degrees.