17 Multiple Choice 1 point 17. A pennant for the sports teams at Walter Johnson High School is in the shape of an isosceles triangle. If the measure of the vertex angle is $$ 18^{\circ} $$, find the measure of each base angle. $$ 18^{\circ}, 144^{\circ} $$ $$ 18^{\circ}, 18^{\circ} $$ $$ 81^{\circ}, 81^{\circ} $$ $$ 162^{\circ} .162^{\circ} $$ Clear my selection

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To determine the measure of each base angle in the isosceles triangle, follow these steps:

1. **Understand the Properties of an Isosceles Triangle:**
   - An isosceles triangle has two equal sides and two equal angles (the base angles).

2. **Set Up the Equation:**
   - Let each base angle be $$ x $$.
   - The sum of all angles in a triangle is $$ 180^{\circ} $$.

3. **Formulate the Equation:**
   $$
   x + x + 18^{\circ} = 180^{\circ}
   $$
   $$
   2x + 18^{\circ} = 180^{\circ}
   $$

4. **Solve for $$ x $$:**
   $$
   2x = 180^{\circ} - 18^{\circ}
   $$
   $$
   2x = 162^{\circ}
   $$
   $$
   x = 81^{\circ}
   $$

Therefore, each base angle measures $$ 81^{\circ} $$.

**Answer:** $$ 81^{\circ}, 81^{\circ} $$
Each base angle is $$ 81^{\circ} $$.

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