Question

current skill $ show answer request h

find the measure of angle 8.
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Explanation:

Step1: Use the property of corresponding angles

Since the two lines are parallel, the angles \(9x - 68\) and \(4x+14\) are equal. So we have the equation \(9x - 68=4x + 14\).

Step2: Solve the equation for \(x\)

Subtract \(4x\) from both sides: \(9x-4x-68 = 4x-4x + 14\), which simplifies to \(5x-68=14\).
Add \(68\) to both sides: \(5x-68 + 68=14 + 68\), so \(5x=82\).
Divide both sides by \(5\): \(x=\frac{82}{5}=16.4\).

Step3: Find the measure of \(\angle8\)

First, find the measure of \(4x + 14\). Substitute \(x = 16.4\) into \(4x+14\): \(4\times16.4+14=65.6+14 = 79.6\).
Since \(\angle8\) and \(4x + 14\) are supplementary (they form a linear - pair), \(\angle8=180-(4x + 14)\).
Another way: \(\angle8\) and \(9x-68\) are supplementary. Substitute \(x = 16.4\) into \(9x-68\): \(9\times16.4-68=147.6-68 = 79.6\). Then \(\angle8=180 - 79.6=100.4\)

Answer:

\(100.4^{\circ}\)