Question

question
∠1 and ∠2 are complementary angles. if ( mangle1=(x - 1)^{circ} ) and ( mangle2=(8x - 26)^{circ} ), then find the measure of ∠2.
answer attempt 1 out of 3

score: 4/5 penalty: 1 off
angle terminology with equations

Explanation:

Step1: Use the property of complementary angles

Complementary angles sum to \(90^{\circ}\). So, \(m\angle1 + m\angle2=90^{\circ}\).
Substitute \(m\angle1=(x - 1)^{\circ}\) and \(m\angle2=(8x - 26)^{\circ}\) into the equation: \((x - 1)+(8x - 26)=90\).

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 of the equation: \(9x-27 + 27=90 + 27\), so \(9x=117\).
Divide both sides by \(9\): \(x=\frac{117}{9}=13\).

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

Substitute \(x = 13\) into \(m\angle2=(8x - 26)^{\circ}\).
\(m\angle2=(8\times13-26)^{\circ}=(104 - 26)^{\circ}=78^{\circ}\).

Answer:

\(78\)