Question

В треугольнике АBС угол А= углу С, М - середина стороны АС. Найдите угол АМB"

Answer 1

т.к. угол А равен углу С, то треугольник АВС - равнобедренный. =>, медиана -это  и высота, и биссектриса.  т.к ВМ - высота, то угол АМВ = 90 градусов

Answer 2

Given Information

We are given a triangle ABC, where angle A is equal to angle C, and M is the midpoint of side AC. We need to find angle AMB.

Solution

To find angle AMB, we can use the fact that the sum of the angles in a triangle is 180 degrees.

Since angle A is equal to angle C, we can denote them as x. Therefore, angle A = angle C = x.

We know that angle AMB + angle B + angle M = 180 degrees.

Since angle A = angle C = x, we can rewrite the equation as:

angle AMB + x + angle M = 180 degrees.

Since M is the midpoint of side AC, we can also say that angle M = angle B.

Substituting angle M = angle B, we get:

angle AMB + x + angle B = 180 degrees.

Simplifying the equation, we have:

2x + angle AMB = 180 degrees.

Now, we can solve for angle AMB:

angle AMB = 180 degrees - 2x.

Therefore, the measure of angle AMB is 180 degrees - 2x.

Note: The exact value of angle AMB cannot be determined without knowing the measure of angle A or angle C.