Question

Равные отрезки MN и AK пересекаются в точке О. Точка О делит эти отрезки по полам. Точки А и М, N и K соединены. Чему равен угол OKN. если ОМА= 35 градусов

Answer 1

Ответ:

решение смотри на фотографии

Answer 2

Given Information

We are given that the line segments MN and AK intersect at point O, and that point O divides these line segments in half. Points A and M, as well as points N and K, are connected. We are asked to find the measure of angle OKN, given that angle OMA is 35 degrees.

Solution

To find the measure of angle OKN, we can use the fact that the sum of the angles in a triangle is 180 degrees. Since we know the measure of angle OMA is 35 degrees, we can find the measure of angle AMO by subtracting 35 degrees from 180 degrees:

Angle AMO = 180 degrees - 35 degrees = 145 degrees.

Since point O divides line segment MN in half, we can conclude that line segment MO is equal in length to line segment NO. Similarly, since point O divides line segment AK in half, line segment AO is equal in length to line segment KO.

Now, let's consider triangle AMO. We know that angle AMO is 145 degrees and that line segment MO is equal in length to line segment NO. This means that angles AMO and AOM are congruent. Therefore, angle AOM is also 145 degrees.

Similarly, in triangle KNO, angle KNO is congruent to angle KON, and both angles are equal to angle AOM, which is 145 degrees.

Since angles KNO and KON add up to 145 degrees, we can find the measure of angle OKN by subtracting 145 degrees from 180 degrees:

Angle OKN = 180 degrees - 145 degrees = 35 degrees.

Therefore, the measure of angle OKN is 35 degrees.

Answer

The measure of angle OKN is 35 degrees.

Note: The sources provided do not contain specific information about the problem at hand. Therefore, the solution is derived using geometric principles and does not require external sources.