Question

В треугольнике ABC угол B равен 90 градусам, AD и CM - биссектрисы, которые пересекаются в точке O. Найдите угол AOM, ответ дайте в градусах. ---СРОЧНО, МНЕ В ШКОЛУ ЧЕРЕЗ ПОЛТОРА ЧАСА

Answer 1

Ответ:

180-90=90

90:2=45°

180-45=135°градусов... надеюсь верно

Answer 2

Triangle ABC and Angle AOM

In triangle ABC, angle B is equal to 90 degrees. The bisectors of angles AD and CM intersect at point O. We need to find the measure of angle AOM in degrees.

Unfortunately, the search results provided by You.com do not contain the specific information needed to solve this problem. However, we can still proceed with solving the problem using the given information.

Solution:

Since AD and CM are bisectors, they divide angles A and C into two equal parts. Let's denote the measure of angle AOM as x.

Since angle B is a right angle, we know that the sum of angles A and C is 90 degrees. Therefore, angle A and angle C are equal to 45 degrees each.

Since AD is a bisector of angle A, it divides angle A into two equal parts. Therefore, angle DAO is equal to angle OAM, which is x/2.

Similarly, since CM is a bisector of angle C, it divides angle C into two equal parts. Therefore, angle CMO is equal to angle OMC, which is x/2.

Now, let's consider triangle AOM. The sum of the angles in a triangle is always 180 degrees. Therefore, we can write the following equation:

x/2 + x/2 + 45 + 45 = 180

Simplifying the equation, we get:

x + 90 = 180

Subtracting 90 from both sides, we find:

x = 90

Therefore, the measure of angle AOM is 90 degrees.

I hope this helps! Let me know if you have any further questions.