Question

apply the linear pair postulate to determine the value of x in the given diagram.

Explanation:

Step1: Recall Linear Pair Postulate

A linear pair of angles sums to \(180^\circ\). So, \(101^\circ+(x + 51)^\circ=180^\circ\).

Step2: Simplify the Equation

Combine like terms: \(101 + x+ 51=180\), which becomes \(x + 152 = 180\).

Step3: Solve for \(x\)

Subtract 152 from both sides: \(x=180 - 152\).

Answer:

\(x = 28\)