Question

6. В треугольнике ДАВС внешние углы при вершинах АиС равны 76 и 144 градусов. Найти внутренние углы при каждой вершине треугольника. ПОМОГИТЕ ПОЖАЛУЙСТА ​

Answer 1

А(внешняя)= 104°
В(внутреняя)=60°
В(внешняя)=120°
С(внешняя)=104°


С (внешняя)= 180°-76°
С (внешняя)= 104°
А (внешняя)= 180°-144°
А (внешняя)= 36°
В (внутреняя)= 180°-(144°+76°) (180°-120°)
В (внешняя)= 180°-60°
В (внешняя)= 120°

Answer 2

Problem Statement

We are given a triangle DAVS with external angles at vertices A and C measuring 76 and 144 degrees, respectively. We need to find the internal angles at each vertex of the triangle.

Solution

To find the internal angles of the triangle, we can use the fact that the sum of the internal angles of any triangle is always 180 degrees.

Let's denote the internal angles at vertices D, A, V, and S as angle D, angle A, angle V, and angle S, respectively.

According to the problem statement, we know the following: - The sum of the external angles at vertices A and C is 360 degrees (since the sum of all external angles of any polygon is always 360 degrees). - The external angle at vertex A is 76 degrees. - The external angle at vertex C is 144 degrees.

Using these facts, we can find the internal angles as follows:

1. Find the external angle at vertex D: - The sum of the external angles at vertices A, D, and V is 360 degrees. - The external angle at vertex A is 76 degrees. - The external angle at vertex V is 180 degrees (since the sum of the internal and external angles at any vertex of a triangle is always 180 degrees). - Therefore, the external angle at vertex D is 360 - 76 - 180 = 104 degrees.

2. Find the internal angle at vertex A: - The sum of the internal and external angles at vertex A is 180 degrees. - The external angle at vertex A is 76 degrees. - Therefore, the internal angle at vertex A is 180 - 76 = 104 degrees.

3. Find the internal angle at vertex V: - The sum of the internal and external angles at vertex V is 180 degrees. - The external angle at vertex V is 180 degrees. - Therefore, the internal angle at vertex V is 180 - 180 = 0 degrees.

4. Find the internal angle at vertex S: - The sum of the internal and external angles at vertex S is 180 degrees. - The external angle at vertex C is 144 degrees. - Therefore, the internal angle at vertex S is 180 - 144 = 36 degrees.

To summarize, the internal angles at each vertex of triangle DAVS are as follows: - angle D = 104 degrees - angle A = 104 degrees - angle V = 0 degrees - angle S = 36 degrees

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