14. What is the measure of the vertex angle of an isosceles triangle if one of its base angles measures $$ 54^{\circ} $$ ? $$ 108^{\circ} $$ $$ 126^{\circ} $$ $$ 72^{\circ} $$ $$ 63^{\circ} $$

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In an **isosceles triangle**, two sides are of equal length, and the angles opposite these sides (base angles) are also equal. Given that one of the base angles measures $$ 54^{\circ} $$, the other base angle will also be $$ 54^{\circ} $$.

The sum of all angles in any triangle is always $$ 180^{\circ} $$. To find the measure of the **vertex angle**, you can use the following calculation:

$$
\text{Vertex Angle} = 180^{\circ} - (\text{Base Angle 1} + \text{Base Angle 2})
$$
$$
\text{Vertex Angle} = 180^{\circ} - (54^{\circ} + 54^{\circ}) = 180^{\circ} - 108^{\circ} = 72^{\circ}
$$

**Answer:** $$ 72^{\circ} $$
The vertex angle is $$ 72^{\circ} $$.

What is the measure of the vertex angle of an isosceles triangle if one of its base angles measures ?

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