Question

numeric 1 point
corresponding angles
solve for x.

Explanation:

Step1: Use vertical angles property

Vertical angles are equal. The angle vertical to \(105^{\circ}\) is also \(105^{\circ}\).

Step2: Use linear - pair property (or supplementary angles for parallel lines)

Since \(MN\parallel OP\) (assumed from the corresponding - angles setup), \((2x - 5)+105 = 180\) (linear - pair of angles formed by a transversal intersecting parallel lines).
$$2x-5 + 105=180$$
$$2x+100 = 180$$

Step3: Solve for \(x\)

Subtract \(100\) from both sides:
$$2x=180 - 100$$
$$2x=80$$
Divide both sides by \(2\):
$$x=\frac{80}{2}$$

Answer:

\(40\)