Question

Развёрнутый угол МРК разделён лучом РА на два угла так,что угол АРК в 3 раза меньше угла МРА.Найдите градусную меру углов МРА и АРК.

Answer 1

Развернутый угол - 180 градусов
Делим на 
1) 1+ 3 = 4 части
2) 180° : 4 = 45° - малый угол - ОТВЕТ
3) 45° * 3 = 135° - большой -  ОТВЕТ

Answer 2

Solution:

Let's denote the measure of angle MRA as x and the measure of angle ARK as y.

Given that the angle ARK is 3 times smaller than the angle MRA, we can express this relationship as:

y = (1/3)x

We also know that the sum of the measures of the angles formed by a straight line is 180 degrees. Therefore, we have:

x + y = 180

Now, we can solve for the measures of the angles MRA and ARK.

First, we'll express y in terms of x using the relationship y = (1/3)x:

x + (1/3)x = 180

Solving for x: x + (1/3)x = 180 4/3x = 180 x = 180 * 3/4 x = 135

So, the measure of angle MRA (x) is 135 degrees.

Now, we can find the measure of angle ARK (y) using the relationship y = (1/3)x:

y = (1/3) * 135 y = 45

So, the measure of angle ARK (y) is 45 degrees.

Therefore, the measure of angle MRA is 135 degrees and the measure of angle ARK is 45 degrees.

This calculation is based on the relationship between the angles formed by a straight line and the given ratio of their measures