Question

На пря­мой AB взята точка M. Луч MD — бис­сек­три­са угла CMB. Из­вест­но, что ∠DMC = 24°. Най­ди­те угол CMA. Ответ дайте в гра­ду­сах.

Answer 1

1вариант
9) 180-2*81=18
10) r=5/(2cos60)=5 или 180-2*60=60 => треугольник равносторонний => АО=ОВ=ВС=5

2вариант
1)угол DMC = 1/2 угла CMB, тогда угол CMB = 81*2=162
2)угол AMC=угол AMB - угол CMB = 180-162=18
Ответ : 18

№10
1)угол АОВ = 180-60*2=60
2)треугольник равносторонний, тогда АВ=АО (радиус) =5см
Ответ: 5 см

Answer 2

Problem Analysis

We are given a line segment AB and a point M on that line segment. The ray MD is the angle bisector of angle CMB, and we know that angle DMC is 24°. We need to find the measure of angle CMA in degrees.

Solution

To find the measure of angle CMA, we can use the fact that the angle bisector of an angle divides the opposite side into two segments that are proportional to the adjacent sides of the angle. In this case, the angle bisector MD divides the side CB into two segments, CM and MB.

Let's assume that the measure of angle CMA is x°. Since MD is the angle bisector of angle CMB, we can write the following proportion:

CM/MB = CD/DB

Since CM and MB are equal segments on the line AB, we can rewrite the proportion as:

CM/CM = CD/DB

Simplifying the equation, we get:

1 = CD/DB

This means that CD is equal to DB. Therefore, triangle CDB is an isosceles triangle, and angle CDB is equal to angle CBD.

Since angle CDB is equal to angle CBD, we can write the following equation:

angle CDB + angle CBD + angle DBC = 180°

Substituting the given value of angle DMC (24°) and the fact that angle CDB is equal to angle CBD, we get:

24° + 24° + angle DBC = 180°

Simplifying the equation, we find:

angle DBC = 180° - 48° = 132°

Since angle DBC is equal to angle CMA, we can conclude that the measure of angle CMA is 132°.

Answer

The measure of angle CMA is 132°.