Question

11
in the figure below, line m and line n are parallel. answer the following questions.

a) what are the angle pairs?

b) find the value of x.

(2x - 10)°
(65 - x)°
line m
line n

Explanation:

Step1: Identify the angle - pair relationship

Since line \(m\) and line \(n\) are parallel, the angles \((65 - x)^{\circ}\) and \((2x-10)^{\circ}\) are alternate - interior angles. Alternate - interior angles are equal.

Step2: Set up the equation

We set up the equation \(65 - x=2x - 10\).

Step3: Solve the equation for \(x\)

Add \(x\) to both sides of the equation: \(65=2x - 10+x\), which simplifies to \(65 = 3x-10\).
Add \(10\) to both sides: \(65 + 10=3x\), so \(75 = 3x\).
Divide both sides by \(3\): \(x=\frac{75}{3}\).

Answer:

\(x = 25\)