Question

current skill $ show answer request help 2 4 x + 44 8 1 3 5 - 4 x + 99 find the measure of angle 2. 5 game credits

Explanation:

Step1: Use the property of corresponding angles

Since the two lines are parallel, \(x + 44=-4x + 99\) (corresponding angles are equal).

Step2: Solve the equation for \(x\)

Add \(4x\) to both sides: \(x+4x + 44=-4x+4x + 99\), so \(5x+44 = 99\).
Subtract \(44\) from both sides: \(5x+44 - 44=99 - 44\), then \(5x=55\).
Divide both sides by \(5\): \(x=\frac{55}{5}=11\).

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

Substitute \(x = 11\) into \(-4x + 99\), so \(\angle5=-4\times11 + 99=-44 + 99 = 55^{\circ}\).

Step4: Use the property of vertical angles

\(\angle1=\angle5 = 55^{\circ}\) (vertical angles are equal).

Step5: Use the property of supplementary angles

Since \(\angle1+\angle2 = 180^{\circ}\) (supplementary angles), then \(\angle2=180^{\circ}-\angle1\).
Substitute \(\angle1 = 55^{\circ}\), so \(\angle2=180 - 55=125^{\circ}\).

Answer:

\(125^{\circ}\)