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

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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