Question

current skill
find the measure of angle 2.
5 game credits

Explanation:

Step1: Use the property of vertical angles and parallel lines

Since the two lines are parallel, \(6x + 30=-7x + 95\) (alternate - interior angles).

Step2: Solve the equation for \(x\)

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Step3: Find the measure of angle \(3\)

Substitute \(x = 5\) into \(6x+30\), we get \(6\times5+30=60\). Then angle \(3 = 60^{\circ}\) (vertical angles are equal).

Step4: Use the linear - pair property

Since angle \(2\) and angle \(3\) form a linear pair (\(\angle2+\angle3 = 180^{\circ}\)), then \(\angle2=180^{\circ}-\angle3\).
Substitute \(\angle3 = 60^{\circ}\), we get \(\angle2=180 - 60=120^{\circ}\)

Answer:

\(120^{\circ}\)