Question

1. find the value of the variable and state the postulate or theorem used to find the value of the variable.

answer attempt 3 out of 10
x =

Explanation:

Step1: Identify the relationship between the angles

The two angles \((3x + 15)^{\circ}\) and \((2x)^{\circ}\) are same - side exterior and interior angles. But since the lines are parallel (as indicated by the arrowheads), they are actually consecutive interior angles (also known as same - side interior angles) and their sum is \(180^{\circ}\) (Consecutive Interior Angles Theorem). So, we can set up the equation \(3x+15 + 2x=180\).

Step2: Simplify the equation

Combine like terms: \((3x + 2x)+15=180\), which gives \(5x+15 = 180\).

Step3: Solve for \(x\)

Subtract \(15\) from both sides: \(5x+15-15 = 180 - 15\), so \(5x=165\). Then divide both sides by \(5\): \(x=\frac{165}{5}=33\).

Answer:

\(x = 33\) (using the Consecutive Interior Angles Theorem)