Question

знайдіть кути рівнобедриного трикутника,якщо кут при його вершині у 4 рази менший за кут при основі срочно!!!;​

Answer 1

кут при вершині 20°

кут при основі 80°

Answer 2

Finding the Angles of an Isosceles Triangle

To find the angles of an isosceles triangle when the angle at its vertex is 4 times smaller than the angle at the base, we can use the following approach:

1. Identify the Relationship Between the Angles: - Let's denote the angle at the base of the isosceles triangle as x and the angle at the vertex as y. - According to the given information, the angle at the vertex is 4 times smaller than the angle at the base. This can be expressed as: y = 4x.

2. Use the Property of Isosceles Triangles: - In an isosceles triangle, the base angles are equal. Therefore, we can denote the two base angles as x and x.

3. Apply the Angle Sum Property of a Triangle: - The sum of the angles in any triangle is always 180 degrees. We can use this property to find the value of x.

4. Calculate the Angles: - We can use the relationship between x and y to find the values of x and y.

Let's proceed with the calculations based on the given information.

Calculation

Using the relationship y = 4x, we can substitute y in terms of x in the equation x + x + y = 180: - 2x + y = 180 - 2x + 4x = 180 (substituting y = 4x) - 6x = 180 - x = 30

Now that we have found the value of x, we can calculate the value of y: - y = 4x - y = 4 * 30 - y = 120

Conclusion

Therefore, the angles of the isosceles triangle are: - The angle at the base (x) = 30 degrees - The angle at the vertex (y) = 120 degrees