# In triangle ABC, the angle is a = 100 degrees, and the angle is C = 40 degrees. Prove that triangle ABC is isosceles.

Consider a triangle ABC.

In this triangle ABC, by condition, it is known that the value of the angle A is 100 degrees, and the value of the angle C is 40 degrees.

In order to prove that the indicated triangle ABC is isosceles, one should recall the rule.

According to this rule, in an isosceles triangle, the angles at the base are equal.

Thus, now we need to find out the value of the angle B.

Let’s write ABC for a given triangle, paying attention to the rule according to which the sum of the values of all angles of any triangle is equal to 180 °.

A + B + C = 180 °.

B = 180 ° – (A + C).

B = 180 ° – (100 ° + 40 °).

B = 180 ° – 140 °.

B = 40 °.

Thus, in a given triangle ABC, the angles A and B are equal.

A = B = 40 °.

This means that in triangle ABC the angles A and B at the base AB are equal.

This means that it has been proven that this triangle is isosceles, since the values of its angles at the base are equal.