Question

∠1 and ∠2 are complementary angles. if ( m∠1=(3x + 7)^{circ} ) and ( m∠2=(5x - 23)^{circ} ), 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 \(m\angle1=(3x + 7)^{\circ}\) and \(m\angle2=(5x - 23)^{\circ}\) into the equation:
\((3x + 7)+(5x - 23)=90\)

Step2: Simplify the left - hand side of the equation

Combine like terms: \(3x+5x+7 - 23=90\), which simplifies to \(8x-16 = 90\).

Step3: Solve for \(x\)

Add \(16\) to both sides: \(8x-16 + 16=90 + 16\), so \(8x=106\).
Divide both sides by \(8\): \(x=\frac{106}{8}=\frac{53}{4}=13.25\).

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

Substitute \(x = 13.25\) into \(m\angle2=(5x - 23)^{\circ}\).
\(m\angle2=5\times13.25-23\)
\(m\angle2=66.25-23\)
\(m\angle2 = 43.25^{\circ}\)

Answer:

\(43.25^{\circ}\)