Question

∠1 and ∠2 are complementary angles. if m∠1=(x + 29)° and m∠2=(3x - 7)°, then find the measure of ∠1.

Explanation:

Step1: Use the property of complementary angles

Complementary angles sum to \(90^{\circ}\). So, \((x + 29)+(3x - 7)=90\).

Step2: Simplify the equation

Combine like - terms: \(x+3x+29 - 7 = 90\), which gives \(4x+22 = 90\).

Step3: Solve for \(x\)

Subtract 22 from both sides: \(4x=90 - 22\), so \(4x = 68\). Then divide by 4: \(x=\frac{68}{4}=17\).

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

Substitute \(x = 17\) into \(m\angle1=(x + 29)^{\circ}\). So \(m\angle1=(17 + 29)^{\circ}=46^{\circ}\).

Answer:

\(46\)