Question

Сума кутів рівнобедреного трикутника та одного з його зовнішніх кутів дорівнює 240°. Знайдіть кути трикутника. Поооммоогиите прошуу

Answer 1

Відповідь:

Пояснення:

Дано
∆АВС-рівнобедрений
<1+<В+<С+<А=240°
Розв'язання
<В+<С+<А=180° - за ознакою трикутника
<1= 240°- ( <В+<С+<А)= 240°-180°= 60°
<С+<1= 180°- як суміжні
<С= 180°-<1= 180°-60°=120°
<В=<А - за ознакою рівнобедреного трикутника
<А+<В = 180°- 120°= 60°
<А=60°:2=30°
В. 120°; 30°;30°

Answer 2

Solution for Finding the Angles of the Triangle

To find the angles of the triangle, we can use the fact that the sum of the interior angles of a triangle is always 180 degrees. We are given that the sum of the base angles of an isosceles triangle and one of its external angles is 240 degrees.

Let's denote the base angles of the isosceles triangle as x and the external angle as y.

We can set up the following equation based on the given information: x + x + y = 240°

Solving for the Angles

We know that the sum of the interior angles of a triangle is 180 degrees. In an isosceles triangle, the base angles are equal. Therefore, we can express the sum of the base angles as 2x.

So, we have the equation: 2x + y = 240°

We also know that the sum of the interior angles of a triangle is 180 degrees: 2x + y = 180°

Calculating the Angles

To solve for the angles, we can use the equation: 2x + y = 180°

Let's solve for x and y: 2x = 180° - y x = (180° - y) / 2

Now, we can substitute the value of x back into the equation 2x + y = 240° to solve for y.

Final Steps

Substitute the value of x back into the equation 2x + y = 240°: (180° - y) + (180° - y) + y = 240° 360° - 2y + y = 240° 360° - y = 240° -y = 240° - 360° -y = -120° y = 120°

Now that we have found the value of y, we can substitute it back into the equation x = (180° - y) / 2 to find the value of x: x = (180° - 120°) / 2 x = 60° / 2 x = 30°

Conclusion

Therefore, the angles of the triangle are: x = 30° x = 30° y = 120°