4. Analyze and Persevere Find the measure of the complement to an $$ 18^{\circ} $$ angle. Explain your answer.

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UpStudy AI · Accepted Answer

To find the measure of the complement of an $$ 18^{\circ} $$ angle, we need to understand the concept of complementary angles. Two angles are considered complementary if the sum of their measures is $$ 90^{\circ} $$.

### Step-by-step solution:

1. **Identify the known angle**: We have an angle $$ A = 18^{\circ} $$.

2. **Set up the equation for complementary angles**: Let $$ C $$ be the measure of the complement of angle $$ A $$. According to the definition of complementary angles, we can write the equation:
   $$
   A + C = 90^{\circ}
   $$

3. **Substitute the known value**: Substitute $$ A = 18^{\circ} $$ into the equation:
   $$
   18^{\circ} + C = 90^{\circ}
   $$

4. **Solve for $$ C $$**: To find $$ C $$, we can rearrange the equation:
   $$
   C = 90^{\circ} - 18^{\circ}
   $$

5. **Perform the calculation**:
   $$
   C = 72^{\circ}
   $$

### Conclusion:
The measure of the complement to an $$ 18^{\circ} $$ angle is $$ 72^{\circ} $$. This means that when you add $$ 18^{\circ} $$ and $$ 72^{\circ} $$, the total is $$ 90^{\circ} $$, confirming that they are complementary angles.
The complement of a $$ 18^{\circ} $$ angle is $$ 72^{\circ} $$.

4. Analyze and Persevere Find the measure of the complement to an \( 18^{\circ} \) angle. Explain your answer.

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