Question

current skill show answer 8 7 6 5 4 -x + 71 8x + 125 1 find the measure of angle 4

Explanation:

Step1: Use vertical angles property

Vertical angles are equal. So, \(8x + 125=-x + 71\).

Step2: Solve the equation for \(x\)

Add \(x\) to both sides: \(8x+x+125=-x+x + 71\), which simplifies to \(9x+125 = 71\).
Subtract \(125\) from both sides: \(9x+125-125=71 - 125\), so \(9x=-54\).
Divide both sides by \(9\): \(x=\frac{-54}{9}=-6\).

Step3: Find the measure of \(\angle4\)

\(\angle4\) and \(-x + 71\) are supplementary (linear - pair). The measure of \(-x + 71\) when \(x = - 6\) is \(-(-6)+71=6 + 71 = 77\).
Since \(\angle4+(-x + 71)=180^{\circ}\), then \(\angle4=180-( - x + 71)\). Substitute \(x=-6\), \(\angle4=180 - 77=103^{\circ}\).

Answer:

\(103^{\circ}\)