Question

given ( mangle5 = 91^{circ} ) and ( mangle2=(8x + 1)^{circ} ), what is the value of ( x )?

Explanation:

Step1: Use the property of corresponding angles

Since \(m\angle5 = 91^{\circ}\), and \(\angle5\) and \(\angle1\) are corresponding angles, so \(m\angle1=91^{\circ}\).

Step2: Use the property of linear - pair angles

\(\angle1\) and \(\angle2\) form a linear pair. So \(m\angle1 + m\angle2=180^{\circ}\).
Substitute \(m\angle1 = 91^{\circ}\) and \(m\angle2=(8x + 1)^{\circ}\) into the equation:
\(91+(8x + 1)=180\).

Step3: Simplify the equation

First, combine like terms: \(8x+92 = 180\).
Then, subtract 92 from both sides: \(8x=180 - 92\), so \(8x=88\).

Step4: Solve for \(x\)

Divide both sides by 8: \(x=\frac{88}{8}=11\).

Answer:

\(x = 11\)