Question

the angles shown are complementary angles. determine the measures of ∠1 and ∠2. what are the measures of ∠1 and ∠2? m∠1 = ° (simplify your answer.) m∠2 = ° (simplify your answer.)

Explanation:

Step1: Recall complementary - angle property

Complementary angles add up to 90°. So, \(x+(14x + 45)=90\).

Step2: Combine like - terms

\(x+14x+45 = 90\) simplifies to \(15x+45 = 90\).

Step3: Isolate the variable term

Subtract 45 from both sides: \(15x=90 - 45\), so \(15x = 45\).

Step4: Solve for x

Divide both sides by 15: \(x=\frac{45}{15}=3\).

Step5: Find the measure of ∠1

Substitute \(x = 3\) into the expression for ∠1. \(m\angle1=14x + 45\), so \(m\angle1=14\times3+45=42 + 45=87\).

Step6: Find the measure of ∠2

Since \(m\angle2=x\), then \(m\angle2 = 3\).

Answer:

\(m\angle1 = 87^{\circ}\)
\(m\angle2 = 3^{\circ}\)