Question

У трикутнику АВС кут С на 22° більший за кут В, а зовнішній кут при вершині А дорівнює 126°. Знайдіть: 1) кут В (у градусах); 2) кут (' (у градусах).​

Answer 1

Ответ:

Внутренние углы треугольника не Смежные с внешним углом в сумме равны градусной мере внешнего угла

<С+<В=126 градусов

<В=Х

<С=Х+22
Х+Х+22=126

2Х+22=126

2Х=126-22

Х=104:2=52

<В=52 градуса

<С=52+22=74 градуса

ИЛИ не через Х

<В=(126-22):2=52 градуса

<С=52*22=74 градуса

Внешний угол и Смежный ему внутренний угол в сумме равны 180 градусов

<А=180-126=54 градуса

Объяснение:

Answer 2

Given Information:

We are given the following information about triangle ABC: - Angle C is 22° larger than angle B. - The external angle at vertex A is 126°.

We need to find: 1) The measure of angle B in degrees. 2) The measure of angle A in degrees.

Solution:

Let's solve the problem step by step.

1) Finding the measure of angle B: Since angle C is 22° larger than angle B, we can represent angle C as B + 22°.

The sum of the angles in a triangle is always 180°. Therefore, we can write the equation: B + (B + 22°) + 126° = 180°

Simplifying the equation: 2B + 148° = 180° 2B = 180° - 148° 2B = 32° B = 32° / 2 B = 16°

Therefore, the measure of angle B is 16°.

2) Finding the measure of angle A: The sum of the angles in a triangle is always 180°. Therefore, we can write the equation: A + B + C = 180°

Substituting the values of B and C: A + 16° + (16° + 22°) = 180° A + 16° + 38° = 180° A + 54° = 180° A = 180° - 54° A = 126°

Therefore, the measure of angle A is 126°.

To summarize: 1) The measure of angle B is 16°. 2) The measure of angle A is 126°.