In an isoselces triangle, the vertex angle is twice either base angle (let the base angle be x in degrees) remember that the sum of angles of a triangle is 180 degrees?
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Since the sum of the interior angles of any triangle adds up to 180∘ and also the base angles of an isosceles triangle are equal,we may let the base angles be x, then the vertex angle is 2x.
∴x+x+2x=180∘.
∴x=45∘.
Therefore the vertex angle is 90∘.
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