Question

find the measure of angle 8.

Explanation:

Step1: Use the property of vertical angles

Vertical angles are equal. So, \(4x + 98=-5x + 35\)

Step2: Solve the equation for \(x\)

Add \(5x\) to both sides: \(4x+5x + 98=-5x+5x + 35\), which simplifies to \(9x+98 = 35\)
Subtract \(98\) from both sides: \(9x+98 - 98=35 - 98\), so \(9x=-63\)
Divide both sides by \(9\): \(x=\frac{-63}{9}=-7\)

Step3: Find the measure of \(\angle5\)

Substitute \(x = - 7\) into \(-5x + 35\): \(-5\times(-7)+35=35 + 35=70\)

Step4: Use the property of vertical angles to find \(\angle8\)

Since \(\angle5\) and \(\angle8\) are vertical angles, \(\angle8=\angle5\)

Answer:

\(70\)