# It is known that the sum of the angles of a triangle is 180 degrees. find the angle at the apex of an isosceles

September 23, 2021 | education

| **It is known that the sum of the angles of a triangle is 180 degrees. find the angle at the apex of an isosceles triangle (in degrees) if its outer angle at the base is 146 degrees.**

1. Vertices of the triangle – A, B, C.

2. We calculate the degree value ∠С, equal to the difference between the expanded angle (180 °) and the external one at this vertex:

∠С = 180 ° – 146 ° = 134 °.

3. ∠С = ∠А, since both of them are adjacent to the AC side (the base of the isosceles triangle).

4. Calculate the degree measure ∠В:

∠В = 180 ° – (∠С + ∠А) = 180 ° – (34 ° + 34 °) = 112 °.

Answer: ∠В is equal to 112 °.

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