Question

В треугольнике АВС угол С равен 116 градусов, AD и ВЕ- биссектрисы, пересикающиеся в точке О. Найти угол АОВ! помогите пожалуйста срочно! очень благодарна буду!

Answer 1

т.к. угол С = 116, значит

угол А + угол В = 180-116 = 64 градуса

т.к. AD и BE - биссектрисы, значит

угол ОВА + угол ОАВ = (угол А + угол В) : 2 = 32 градуса

угол ВОА = 180 - (угол ОВА + угол ОАВ) = 180 - 32 = 148 градусов

Answer 2

Given Information

We are given a triangle ABC, where angle C is 116 degrees. AD and BE are the bisectors of angles A and B, respectively, and they intersect at point O. We need to find angle AOV.

Solution

To find angle AOV, we can use the angle bisector theorem. According to this theorem, the ratio of the lengths of the segments formed by the intersection of an angle bisector in a triangle is equal to the ratio of the lengths of the sides opposite those angles.

Let's denote the length of segment AD as x and the length of segment BE as y. Then, we can write the following equations:

AC/BC = AD/BD AB/BC = AE/BE

Since AD and BE are bisectors, we know that AD/BD = AE/BE = 1.

Substituting these values into the equations, we get:

AC/BC = 1 AB/BC = 1

Since the ratios are equal to 1, we can conclude that AC = BC and AB = BC.

Now, let's consider triangle ABC. Since AC = BC, angle A = angle B. Let's denote this angle as x.

Since angle C is 116 degrees, we can write the equation:

x + x + 116 = 180

Simplifying the equation, we get:

2x + 116 = 180 2x = 180 - 116 2x = 64 x = 32

Therefore, angle A = angle B = 32 degrees.

Now, let's consider triangle AOB. We know that angle A = angle B = 32 degrees. Since angle A + angle B + angle O = 180 degrees, we can write the equation:

32 + 32 + angle O = 180

Simplifying the equation, we get:

64 + angle O = 180 angle O = 180 - 64 angle O = 116

Therefore, angle AOV is equal to 116 degrees.

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