Question

use the information in the diagram to solve for x.

Explanation:

Step1: Use the linear - pair relationship

Since \(8x\) and \(2(10x + 6)\) form a linear pair, their sum is \(180^{\circ}\). So, \(8x+2(10x + 6)=180\).

Step2: Expand the equation

Expand \(2(10x + 6)\) using the distributive property \(a(b + c)=ab+ac\). We get \(8x+20x+12 = 180\).

Step3: Combine like terms

Combine the \(x\) - terms: \((8x + 20x)+12=180\), which simplifies to \(28x+12 = 180\).

Step4: Isolate the variable term

Subtract \(12\) from both sides of the equation: \(28x+12−12=180−12\). So, \(28x=168\).

Step5: Solve for \(x\)

Divide both sides by \(28\): \(x=\frac{168}{28}\).

Answer:

\(x = 6\)