Question

solve for x.

Explanation:

Step1: Use the property of vertical angles

Vertical angles are equal. The angle \(80^{\circ}\) and the angle adjacent to \(15x + 10\) are vertical angles. The sum of adjacent angles forming a linear - pair is \(180^{\circ}\). So, \(80+(15x + 10)=180\).

Step2: Simplify the equation

First, combine like terms in the left - hand side of the equation: \(80+15x + 10=15x+(80 + 10)=15x + 90\). The equation becomes \(15x+90 = 180\).

Step3: Isolate the variable term

Subtract 90 from both sides of the equation: \(15x+90-90=180 - 90\). So, \(15x=90\).

Step4: Solve for \(x\)

Divide both sides of the equation by 15: \(x=\frac{90}{15}\).

Answer:

\(x = 6\)