Question

Дан треугольник АВС AD биссиктриса AD=DC уголС=20 градусов Найти углы АВС.

Answer 1

Так как АД = ДС , значит  треугольник АДС равнобедренный. В равнобедренном треугольнике углы при основании равны, значит угол ДАС = углу С = 20 градусов. Так как АД биссектрисса, то угол А = 40 градусов. Угол В = 180 - (А+С), угол В = 180-(40+20) = 120 градусов.

Ответ: А = 40, В = 120, С = 20 

Answer 2

Given Information:

We are given a triangle ABC, where AD is the bisector of angle C, AD = DC, and angle C = 20 degrees. We need to find the angles of triangle ABC.

Solution:

To find the angles of triangle ABC, we can use the properties of triangles and the given information.

Let's denote angle A as A, angle B as B, and angle C as C.

From the given information, we know that AD is the bisector of angle C and AD = DC. This implies that angles ADB and ADC are congruent. Therefore, angle ADB = angle ADC.

Using the property of angles on a straight line, we know that the sum of angles ADB and ADC is 180 degrees. So, we can write:

ADB + ADC = 180 degrees

Since angle ADB = angle ADC, we can rewrite the equation as:

2 * ADB = 180 degrees

Simplifying the equation, we find:

ADB = 90 degrees

Now, we can use the fact that the sum of angles in a triangle is 180 degrees. So, we have:

ADB + A + B = 180 degrees

Substituting the value of ADB, we get:

90 degrees + A + B = 180 degrees

Simplifying the equation, we find:

A + B = 90 degrees

Since angle C is given as 20 degrees, we can write:

A + B + C = 90 degrees + 20 degrees

Simplifying the equation, we find:

A + B + C = 110 degrees

Now, we have two equations:

1. A + B = 90 degrees 2. A + B + C = 110 degrees

Subtracting equation 1 from equation 2, we get:

C = 20 degrees

Substituting the value of C in equation 1, we find:

A + B = 90 degrees - 20 degrees

Simplifying the equation, we find:

A + B = 70 degrees

Now, we have two equations:

1. A + B = 70 degrees 2. A + B + C = 110 degrees

Subtracting equation 1 from equation 2, we get:

C = 40 degrees

Finally, substituting the value of C in equation 1, we find:

A + B = 70 degrees - 40 degrees

Simplifying the equation, we find:

A + B = 30 degrees

Therefore, the angles of triangle ABC are:

A = 30 degrees B = 40 degrees C = 20 degrees

Answer:

The angles of triangle ABC are: A = 30 degrees B = 40 degrees C = 20 degrees