Question

what is the value of x?
x = 2.25
x = 11.25
x = 13
x = 22

Explanation:

Step1: Use vertical angles and straight - line angle property

We know that the angle \(6x + 1\) and the angle adjacent to \(79^{\circ}\) and \((2x + 10)^{\circ}\) form a straight - line (sum to \(180^{\circ}\)). First, find the angle adjacent to \(79^{\circ}\) which is \(180^{\circ}-79^{\circ}=101^{\circ}\). Then, by the property of angles around a point (sum of angles on a straight - line), we have \((6x + 1)+(2x + 10)+101=180\).

Step2: Simplify the equation

Combine like terms: \(6x+2x+1 + 10+101=180\), which simplifies to \(8x+112 = 180\).

Step3: Solve for \(x\)

Subtract \(112\) from both sides: \(8x=180 - 112\), so \(8x=68\). Then divide both sides by \(8\): \(x=\frac{68}{8}=13\).

Answer:

\(x = 13\) (the third option)