From the condition we know that the angle at the base of an isosceles triangle is 45 °. In order to find the angle at the vertex, we will use the property of angles at the base of an isosceles triangle and the theorem on the sum of the angles of a triangle.
So, the angles at the base of an isosceles triangle are equal to each other.
And the theorem on the sum of the angles of a triangle says that the sum of the angles of a triangle is 180 °.
So, in order to find the angle at the apex of the triangle, we will subtract the sum of the angles at the base from 180 °.
180 ° – (45 ° + 45 °) = 180 ° – 90 ° = 90 ° angle at the apex of an isosceles triangle.
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