Question

Кут при основі рівнобедреного трикутника в 4 рази менший від зовнішнього кута, суміжного з ним. Знайдіть кут при вершині цього трикутника​

Answer 1

Відповідь: 108°

Пояснення: фото

Answer 2

#### Finding the Angle at the Vertex of an Isosceles Triangle To find the angle at the vertex of an isosceles triangle, we need to use the information given in the question. According to the question, the angle at the base of the triangle is 4 times smaller than the external angle adjacent to it. Let's assume that the external angle adjacent to the base is represented by **x**. Since the angle at the base is 4 times smaller than the external angle, we can express it as **4x**. Now, let's find the sum of the angles in an isosceles triangle. An isosceles triangle has two equal angles at the base, which we can represent as **y**. The angle at the vertex of the triangle can be represented as **z**. The sum of the angles in a triangle is always 180 degrees. Therefore, we can write the equation: **y + y + z = 180** Since the angle at the base is 4 times smaller than the external angle, we can write: **y = 4x** Substituting this value into the equation, we get: **4x + 4x + z = 180** Simplifying the equation, we have: **8x + z = 180** To find the value of **z**, we need to know the value of **x**. Unfortunately, the value of **x** is not given in the question or search results. Therefore, we cannot determine the exact value of the angle at the vertex of the triangle without additional information. If you have any additional information or if there's anything else I can help you with, please let me know!