Question

зовнішні кут трикутника при вершині рівнобедреного трикутника дорівнює 150.Знайдіть кут при основі цього трикутника .​

Answer 1

сума зовнішнього і внутрішнього кутів 180 °

тобто кут при вершині  = 180° - 150° = 30°

отже кути при основі :

(180 - 30)/2 = 75°

кут при основі трикутника 75 °

Answer 2

Finding the Angle at the Base of an Isosceles Triangle

To find the angle at the base of an isosceles triangle when the exterior angle at the vertex of the triangle is given, we can use the property that the exterior angle at the vertex of an isosceles triangle is equal to the sum of the two opposite interior angles.

Given that the exterior angle at the vertex of the isosceles triangle is 150 degrees, we can find the angle at the base using the following steps:

1. Calculate the Interior Angle: - The exterior angle at the vertex of the isosceles triangle is equal to the sum of the two opposite interior angles. - Let's denote the angle at the base of the triangle as x. - Using the property mentioned above, we can set up the equation: 150 = 2x, where 2x represents the sum of the two opposite interior angles.

2. Solve for the Angle at the Base: - To find the value of x, we can solve the equation 150 = 2x for x.

- Solving for x: - Divide both sides of the equation by 2: 150 / 2 = x - Therefore, x = 75 degrees.

Therefore, the angle at the base of the isosceles triangle is 75 degrees.