# In a triangle abc, the angle a is 55 ° ab = bc. Find the angle at the vertex b.

October 3, 2021 | education

| Before calculating what the angle B is equal to, let us pay attention to which triangle is given according to the condition of the problem.

Since, by condition, the sides AB and BC of this triangle are equal, the triangle is isosceles.

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

Thus, the magnitude of the angle A is equal to the magnitude of the angle C.

Now let’s make up the equality.

In this case, remember the rule, in which the sum of all sides of a triangle is 180 °.

A + B + C = 180 °.

Since A + C = 2A, then we will write.

B + 2A = 180 °.

B = 180 ° – 2A.

Now let’s substitute the numerical value of the angle A into this equality.

B = 180 ° – 2 × 55 °.

B = 180 ° – 110 °.

B = 70 °.

Answer: B = 70 °.

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