Question

x = 12.7
ways to rewrite expressions
equation
transformations
enter the measure of the angle.
degrees

Explanation:

Step1: Use the straight - line angle property

Since \(URQ\) is a straight line, the sum of angles \((3x + 24)^{\circ}\), \((7x-22)^{\circ}\) and \(51^{\circ}\) 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 \(10x+(24 - 22+51)=180\), then \(10x + 53=180\).

Step3: Solve for \(x\)

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

Step4: Find the measure of \((7x - 22)^{\circ}\)

Substitute \(x = 12.7\) into \(7x-22\). We get \(7\times12.7-22\). First, calculate \(7\times12.7 = 88.9\). Then \(88.9-22=66.9\).

Answer:

\(66.9\)