Question

recall that two angles are complementary if the sum of their measures is 90°.
find the measures of two complementary angles if one angle is 6° more than three times the other angle.
the smaller angle measures □°.

Explanation:

Step1: Set up the equation

Let the smaller angle be \(x\). Then the larger angle is \(3x + 6\). Since the two angles are complementary, \(x+(3x + 6)=90\).

Step2: Simplify the equation

Combine like - terms: \(4x+6 = 90\).
Subtract 6 from both sides: \(4x=90 - 6=84\).

Step3: Solve for \(x\)

Divide both sides by 4: \(x=\frac{84}{4}=21\).

Answer:

\(21\)