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, \(x+(11x + 6)=90\).

Step2: Combine like - terms

\(x+11x+6 = 90\) simplifies to \(12x+6 = 90\).

Step3: Solve for \(x\)

Subtract 6 from both sides: \(12x=90 - 6=84\). Then divide both sides by 12: \(x=\frac{84}{12}=7\).

Step4: Find the measure of \(\angle1\)

\(\angle1=11x + 6\). Substitute \(x = 7\) into the expression: \(m\angle1=11\times7+6=77 + 6=83\).

Step5: Find the measure of \(\angle2\)

\(\angle2=x\). Since \(x = 7\), \(m\angle2=7\).

Answer:

\(m\angle1 = 83\)
\(m\angle2 = 7\)