Question 1012489
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the vertex angle of an isosceles triangle is twice as large as one of the base angles. Find the measure of the vertex angles.
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<U>Answer</U>. 90 degrees.


<U>Solution</U>

Let m be the measure of the angle at the base. Then the other angle at the base has the same measure m as the triangle is isosceles.

The vertex angle is 2m according to the condition.

Since the sum of interior angles of a triangle is 189 degrees, it gives you an equation

m + m + 2m = 180,   or  4m = 180.

Hence, m = {{{180/4}}} = 45 degrees for the angle at the base.

It gives 90 degrees for the vertex angle.

The problem is solved.
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