Question

what is the value of x? x = 2.25 x = 11.25 x = 13 x = 22 (2x + 10)° (6x + 1)° 79°

Explanation:

Step1: Use vertical angles property

Vertical angles are equal. The angle \((2x + 10)^{\circ}\) and the angle adjacent to \((6x+1)^{\circ}\) and \(79^{\circ}\) form a linear - pair. First, find the measure of the angle adjacent to \((6x + 1)^{\circ}\) and \(79^{\circ}\).
The sum of angles on a straight line is \(180^{\circ}\). Let \(y\) be the angle adjacent to \((6x + 1)^{\circ}\) and \(79^{\circ}\), then \(y=180-(6x + 1+79)=180-(6x + 80)=100 - 6x\).
Since \(y=(2x + 10)\) (vertical angles are equal), we get the equation \(100-6x=2x + 10\).

Step2: Solve the equation for \(x\)

Add \(6x\) to both sides of the equation \(100-6x=2x + 10\):
\(100=2x+10 + 6x\).
Combine like terms: \(100=8x + 10\).
Subtract \(10\) from both sides: \(100-10=8x\), so \(90 = 8x\).
Divide both sides by \(8\): \(x=\frac{90}{8}=11.25\).

Answer:

\(x = 11.25\)