Question

6 what is the value of x? show your work. 156° (3x + 36)° solution 126 lesson 6 describe angle relationships

Explanation:

Step1: Find the adjacent angle of \(156^{\circ}\)

Since adjacent angles on a straight line sum to \(180^{\circ}\), the adjacent angle of \(156^{\circ}\) is \(180 - 156=24^{\circ}\)

Step2: Use the property of alternate - interior angles

The angle \(24^{\circ}\) and \((3x + 36)^{\circ}\) are alternate - interior angles. So \(3x+36 = 24\)

Step3: Solve the equation for \(x\)

Subtract \(36\) from both sides: \(3x=24 - 36\), \(3x=- 12\). Then divide both sides by \(3\): \(x=\frac{-12}{3}=-4\)

Answer:

\(x = - 4\)