Recall that two angles are complementary if the sum of their measures is $90^{\circ}$. Find the measures of two complementary angles if one angle is nine times the other angle.
Smaller angle $=$ $7^{\circ}$
Larger angle $=$
Answer
So, the smaller angle is \(\boxed{9}\) degrees and the larger angle is \(\boxed{81}\) degrees.
Step 1 ：Let the smaller angle be \(x\) and the larger angle be \(9x\).
Step 2 ：Since the two angles are complementary, their sum is 90 degrees. So, we can write the equation: \(x + 9x = 90\).
Step 3 ：Combine like terms to get: \(10x = 90\).
Step 4 ：Divide both sides by 10 to solve for \(x\): \(x = \frac{90}{10} = 9\).
Step 5 ：Substitute \(x = 9\) into the expression for the larger angle to get: \(9x = 9 * 9 = 81\).
Step 6 ：Check the solution by adding the two angles: \(9 + 81 = 90\).
Step 7 ：So, the smaller angle is \(\boxed{9}\) degrees and the larger angle is \(\boxed{81}\) degrees.
