Question

∠1 and ∠2 are complementary angles. if m∠1=(3x - 7)° and m∠2=(5x - 23)°, then find the measure of ∠2.

Explanation:

Step1: Recall complementary - angle property

Complementary angles sum to 90°. So, \(m\angle1 + m\angle2=90^{\circ}\).
Substitute the given expressions: \((3x - 7)+(5x - 23)=90\).

Step2: Simplify the left - hand side

Combine like terms: \(3x+5x-7 - 23 = 90\), which gives \(8x-30 = 90\).

Step3: Solve for \(x\)

Add 30 to both sides: \(8x-30 + 30=90 + 30\), so \(8x=120\).
Divide both sides by 8: \(x=\frac{120}{8}=15\).

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

Substitute \(x = 15\) into the expression for \(m\angle2\): \(m\angle2=(5x - 23)^{\circ}\).
\(m\angle2=(5\times15 - 23)^{\circ}=(75 - 23)^{\circ}=52^{\circ}\).

Answer:

\(52^{\circ}\)