Question

current skill
show answer request
1
2
3
9x - 68
5
4x + 14
7
8
find the measure of angle 8.

Explanation:

Step1: Use the property of corresponding angles

Since the two lines are parallel, \(9x - 68=4x + 14\).

Step2: Solve the equation for \(x\)

Subtract \(4x\) from both sides: \(9x-4x - 68=4x-4x + 14\), which gives \(5x-68 = 14\).
Add \(68\) to both sides: \(5x-68 + 68=14 + 68\), so \(5x=82\), then \(x = 18\).

Step3: Find the measure of \(4x + 14\)

Substitute \(x = 18\) into \(4x + 14\): \(4\times18+14=72 + 14=86\).

Step4: Use the property of supplementary angles

Angle \(8\) and \(4x + 14\) are supplementary. Let the measure of angle \(8\) be \(y\), then \(y+(4x + 14)=180\).
Since \(4x + 14 = 86\), then \(y=180-(4x + 14)=180 - 86=94\).

Answer:

\(94^{\circ}\)