Question

∠1 and ∠2 are complementary angles. if (mangle1=(5x + 27)^{circ}) and (mangle2=(4x - 18)^{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 \(m\angle1=(5x + 27)^{\circ}\) and \(m\angle2=(4x - 18)^{\circ}\) into the equation: \((5x + 27)+(4x - 18)=90\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(5x+4x+27 - 18=90\), which simplifies to \(9x + 9 = 90\).

Step3: Solve for \(x\)

Subtract 9 from both sides: \(9x=90 - 9\), so \(9x = 81\).
Divide both sides by 9: \(x=\frac{81}{9}=9\).

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

Substitute \(x = 9\) into the expression for \(m\angle1\): \(m\angle1=(5x + 27)^{\circ}=(5\times9 + 27)^{\circ}\).
Calculate \(5\times9+27=45 + 27=72^{\circ}\).

Answer:

\(72^{\circ}\)