Question

∠1 and ∠2 are complementary angles. if (mangle1=(x - 1)^{circ}) and (mangle2=(8x - 26)^{circ}), then find the measure of ∠2.

Explanation:

Step1: Recall complementary - angle property

Complementary angles add up to 90°. So, \(m\angle1 + m\angle2=90^{\circ}\).
\((x - 1)+(8x - 26)=90\)

Step2: Simplify the left - hand side

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

Step3: Solve for \(x\)

Add 27 to both sides: \(9x-27 + 27=90 + 27\), 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 \(m\angle2\). \(m\angle2=(8x - 26)^{\circ}\), so \(m\angle2=(8\times13 - 26)^{\circ}=(104 - 26)^{\circ}=78^{\circ}\).

Answer:

\(78^{\circ}\)