Question

solve for x.

Explanation:

Step1: Use the property of vertical angles

Vertical angles are equal. The angle adjacent to \(105^{\circ}\) (on a straight - line) is \(180 - 105=75^{\circ}\). Since \(MN\parallel OP\), the angle \((2x - 5)^{\circ}\) and the angle adjacent to \(105^{\circ}\) are equal (corresponding angles). So, \(2x-5 = 75\).

Step2: Solve the equation for \(x\)

Add \(5\) to both sides of the equation \(2x-5 = 75\):
\(2x-5 + 5=75 + 5\), which simplifies to \(2x=80\).
Divide both sides by \(2\): \(x=\frac{80}{2}\).

Answer:

\(x = 40\)