Question

Луч АС делит развернутый угол МАN на два угла МАС и САN. Найдите градусную меру этих углов,если угол САN меньше угла МАС в 2,6 раза.

Answer 1

 Пусть угол САN =х, тогда угол MAC=2,6х

По условию угол MAN=180⁰

х+2,6х=180;

3,6х=180;

х=180:3,6;

х=50° - угол САN

50·2,6=130°-угол MAC.

Answer 2

Problem Statement

We are given that a ray AS divides the interior angle MAN into two angles MAS and SAN. We need to find the measure of these angles in degrees, if the measure of angle SAN is 2.6 times smaller than the measure of angle MAS.

Analysis

Let the measure of angle MAS be x degrees. Then, according to the question, the measure of angle SAN is 2.6 times smaller than angle MAS. So, the measure of angle SAN is x/2.6 degrees.

Solution

We know that the total measure of an interior angle of a triangle is 180 degrees. Therefore, x + x/2.6 = 180 1.6x = 180 x = 112.5 degrees

Therefore, the measure of angle MAS is 112.5 degrees. And the measure of angle SAN is x/2.6 = 112.5/2.6 = 43.1 degrees.