Question

use the relationship you determined to write an equation to help you solve for x.

Explanation:

Step1: Use the straight - angle property

The sum of angles around a point on a straight line is \(180^{\circ}\). So, \((3x + 24)+(7x-22)+51=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \((3x+7x)+(24 - 22+51)=180\), which gives \(10x+(2 + 51)=180\), then \(10x+53 = 180\).

Step3: Solve for \(x\)

Subtract 53 from both sides: \(10x=180 - 53\), so \(10x=127\). Then divide both sides by 10: \(x=\frac{127}{10}=12.7\).

Answer:

\(x = 12.7\)