Question

У рівнобедреному трикутнику АВС з основою АС сума двох нерівних кутів дорівнює 166 градусів.Знайдіть усі кути цього трикутника. Розв`яжіть будьласка задачу.Буду вдячний вам

Answer 1

Кут А=180-166=34
Оскільки АBC-рівнобедр то кут С=А=34
кут В=166-34=132

Answer 2

Problem Analysis

We are given an isosceles triangle ABC with base AC, and the sum of two unequal angles is 166 degrees. We need to find all the angles of this triangle.

Solution

Let's assume that angle A = angle C = x degrees, and angle B = y degrees.

Since the sum of two unequal angles is 166 degrees, we can write the following equation:

x + y = 166

Since triangle ABC is isosceles, angles A and C are equal. Therefore, we can write:

x = y

Substituting this into the equation above, we get:

x + x = 166 2x = 166 x = 83

So, angle A = angle C = 83 degrees.

Since the sum of the angles in a triangle is always 180 degrees, we can find angle B:

angle B = 180 - (angle A + angle C) angle B = 180 - (83 + 83) angle B = 180 - 166 angle B = 14

Therefore, the angles of triangle ABC are: - angle A = angle C = 83 degrees - angle B = 14 degrees

Conclusion

In the given isosceles triangle ABC with base AC, the sum of two unequal angles is 166 degrees. The angles of this triangle are: - angle A = angle C = 83 degrees - angle B = 14 degrees