Question

given the following parallel lines cut by a transversal, what is the value of x?
(3x + 15)°
105°
x = type your answer...

Explanation:

Step1: Use the property of same - side exterior and interior angles

When two parallel lines are cut by a transversal, the sum of same - side exterior and interior angles is \(180^{\circ}\). So, \((3x + 15)+105 = 180\).

Step2: Simplify the equation

First, combine like terms: \(3x+15 + 105=3x + 120\). Then the equation becomes \(3x+120 = 180\).
Subtract \(120\) from both sides: \(3x+120-120=180 - 120\), which gives \(3x=60\).

Step3: Solve for \(x\)

Divide both sides of the equation \(3x = 60\) by \(3\): \(x=\frac{60}{3}\).

Answer:

\(20\)