How to find an angle in an acute / obtuse isosceles triangle - ISEE Upper Level Mathematics Achievement

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Question

One of the base angles of an isosceles triangle is $42^{\circ}$ . Give the measure of the vertex angle.

Answer

The base angles of an isosceles triangle are always equal. Therefore both base angles are $42^{\circ}$ .

Let the measure of the third angle. Since the sum of the angles of a triangle is $180^{\circ}$ , we can solve accordingly:

$42+42+x=180\Rightarrow x=180-84\Rightarrow x=96^{\circ}$

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