Question

∠1 and ∠2 are complementary angles. if (mangle1=(5x + 27)^{circ}) and (mangle2=(7x - 21)^{circ}), then find the measure of ∠1. answer attempt 1 out of 3

Explanation:

Step1: Recall complementary - angle property

Complementary angles sum to 90°. So, \(m\angle1 + m\angle2=90^{\circ}\). Substitute the given expressions: \((5x + 27)+(7x-21)=90\).

Step2: Simplify the left - hand side

Combine like terms: \(5x+7x + 27-21=90\), which simplifies to \(12x + 6=90\).

Step3: Solve for \(x\)

Subtract 6 from both sides: \(12x=90 - 6=84\). Then divide both sides by 12: \(x=\frac{84}{12}=7\).

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

Substitute \(x = 7\) into the expression for \(m\angle1\): \(m\angle1=5x+27=5\times7 + 27=35+27=62^{\circ}\).

Answer:

\(62^{\circ}\)