# One of the outer corners of an isosceles triangle is 70 degrees. Find the corners of the triangle.

September 30, 2021 | education

| Let △ ABC be given, in which AB = BC, then AC is the base of this triangle, therefore ∠A = ∠C as angles at the base of an isosceles triangle.

1. Let ∠BAD = 70 ° be the outer angle at the vertex A, then ∠A = 180 ° – ∠BAD = 180 ° – 70 ° = 110 °.

If ∠A = ∠C, then ∠C = 110 °.

Two angles at the base of an isosceles triangle cannot be obtuse, since a triangle cannot have two obtuse angles.

2. Let ∠CBD = 70 ° be the outer angle at vertex B, then ∠B = 180 ° – ∠CBD = 180 ° – 70 ° = 110 °.

Since ∠A = ∠C, we denote them as x. By the theorem on the sum of the angles of a triangle:

∠A + ∠B + ∠C = 180 °;

x + 110 ° + x = 180 °;

2 * x = 180 ° – 110 °;

2 * x = 70 °;

x = 70 ° / 2;

x = 35 °.

Thus, ∠A = ∠C = x = 35 °.

Answer: ∠A = 35 °, ∠B = 110 °, ∠C = 35 °.

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