Question

current skill $ find the measure of angle 8. label optional skill code 1120012

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. Angle 1 and angle 5 are vertical angles, so \(-x + 74=-5x + 98\).

Step2: Solve the equation for x

Add \(5x\) to both sides: \(-x+5x + 74=-5x+5x + 98\), which simplifies to \(4x+74 = 98\). Then subtract 74 from both sides: \(4x+74 - 74=98 - 74\), getting \(4x=24\). Divide both sides by 4: \(x = 6\).

Step3: Find the measure of angle 5

Substitute \(x = 6\) into the expression for angle 5: \(-5x+98=-5\times6 + 98=-30 + 98 = 68\).

Step4: Use linear - pair property

Angle 5 and angle 8 form a linear - pair (sum to 180°). Let the measure of angle 8 be \(y\). Then \(y+68 = 180\). Subtract 68 from both sides: \(y=180 - 68=112\).

Answer:

112