Question

∠1 and ∠2 are complementary angles. if m∠1=(x - 22)° and m∠2=(x - 24)°, then find the measure of ∠2.

Explanation:

Step1: Use the property of complementary angles

Complementary angles sum to \(90^{\circ}\). So, \(m\angle1 + m\angle2=90^{\circ}\).
Substitute \(m\angle1=(x - 22)^{\circ}\) and \(m\angle2=(x - 24)^{\circ}\) into the equation:
\((x - 22)+(x - 24)=90\)

Step2: Simplify the left - hand side of the equation

Combine like terms: \(x+x-22 - 24=90\), which simplifies to \(2x-46 = 90\)

Step3: Solve for \(x\)

Add \(46\) to both sides of the equation: \(2x-46 + 46=90 + 46\), so \(2x=136\)
Divide both sides by \(2\): \(x=\frac{136}{2}=68\)

Step4: Find the measure of \(\angle2\)

Substitute \(x = 68\) into \(m\angle2=(x - 24)^{\circ}\)
\(m\angle2=(68 - 24)^{\circ}=44^{\circ}\)

Answer:

\(44^{\circ}\)