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
