Question

∠1 and ∠2 are complementary angles. if m∠1 = (x - 1)° and m∠2 = (8x - 26)°, then find the measure of ∠2.

Explanation:

Step1: Use the property of complementary angles

Complementary angles sum to \(90^{\circ}\). So, \((x - 1)+(8x - 26)=90\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(x+8x-1 - 26=90\), which gives \(9x-27 = 90\).

Step3: Solve for \(x\)

Add \(27\) to both sides: \(9x=90 + 27\), so \(9x=117\). Then divide both sides by \(9\): \(x=\frac{117}{9}=13\).

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

Substitute \(x = 13\) into the expression for \(\angle2\): \(m\angle2=(8x - 26)^{\circ}\). So, \(m\angle2=(8\times13-26)^{\circ}\). First, calculate \(8\times13 = 104\), then \(104-26=78\).

Answer:

\(78^{\circ}\)