Question

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

Explanation:

Step1: Use the property of complementary angles

Complementary angles sum to \(90^{\circ}\). So, \(m\angle1 + m\angle2=90^{\circ}\).
Substitute \(m\angle1=(x + 29)^{\circ}\) and \(m\angle2=(3x - 7)^{\circ}\) into the equation: \((x + 29)+(3x - 7)=90\).

Step2: Simplify the left - hand side of the equation

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

Step3: Solve for \(x\)

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

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

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

Answer:

\(46^{\circ}\)