# In triangle ABC, sides AB and BC are equal, and the outer head at apex C = 123 degrees. Find the value of angle B.

May 28, 2021 | education

| Since in this triangle the sides AB and BC are equal, then this triangle is isosceles, and in an isosceles triangle the angles at the base are equal:

∠А = ∠С.

Since the sum of the outer and inner angles of the triangle at one vertex is 180º, and the outer angle at the vertex C is 123º, then:

∠С = 180º – φ;

∠С = 180º – 123º = 57º;

∠А = ∠С = 57º.

Since the sum of all angles of a triangle is 180º, then:

∠В = 180º – ∠А – ∠С;

∠В = 180º – 57º – 57º = 66º.

Answer: the angle ∠B is equal to 66º.

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