# In the triangle ABC, AC = BC. The external angle at vertex B is 121 °. Find the angle C.

May 31, 2020 | Education

| ∠CBA – is adjacent to the outer corner, therefore 180 ° = ∠CBA + 121 °

∠CBA = 180 ° -121 ° = 59 °

Since AC = BC, the triangle ABC is isosceles.

Hence ∠CBA = ∠CAB = 59 ° (by the property of an isosceles triangle)

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

180 ° = ∠CBA + ∠CAB + ∠C

180 ° = 59 ° + 59 ° + ∠C

∠C = 62 °

Answer: 62

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