# In the triangle ABC, AC = BC. The external angle at vertex B is 154 °. Find the angle C.

May 31, 2020 | Education

| ∠CBA – is adjacent to the outer corner, therefore 180 ° = ∠CBA + 154 °

∠CBA = 180 ° -154 ° = 26 °

Since AC = BC, the triangle ABC is isosceles.

So ∠CBA = ∠CAB = 26 ° (by the property of an isosceles triangle)

By the theorem on the sum of the angles of a triangle:

180 ° = ∠CBA + ∠CAB + ∠C

180 ° = 26 ° + 26 ° + ∠C

∠C = 128 °

Answer: 128

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