Question

two angles are complementary. one angle is 20° less than three times the other angle. find the measures of the angles. the smaller angle is (square^{circ}). part 1 of 2 progress 0/2 incorrect 2 tries left. please try again.

Explanation:

Step1: Let the smaller angle be $x$.

The other angle is $3x - 20$.

Step2: Use the complementary - angle property.

Since the two angles are complementary, their sum is $90^{\circ}$. So, $x+(3x - 20)=90$.

Step3: Simplify the equation.

Combine like - terms: $x + 3x-20=90$, which gives $4x-20 = 90$.

Step4: Solve for $x$.

Add 20 to both sides of the equation: $4x=90 + 20=110$. Then divide both sides by 4: $x=\frac{110}{4}=27.5$.

Answer:

$27.5$