Question

3.3 extra practice
in exercises 1 and 2, find the value of x that makes m || n. explain your reasoning.
1.
2.

Explanation:

Exercise 1

Step1: Use the consecutive - interior angles theorem

If \(m\parallel n\), then the sum of consecutive - interior angles is \(180^{\circ}\). So, \(95+(8x + 55)=180\).

Step2: Simplify the left - hand side of the equation

\(95+8x+55=180\), which simplifies to \(8x + 150=180\).

Step3: Solve for \(x\)

Subtract \(150\) from both sides: \(8x=180 - 150\), so \(8x=30\). Then \(x=\frac{30}{8}=\frac{15}{4}=3.75\).

Step1: Use the corresponding angles relationship

First, find the angle adjacent to \(130^{\circ}\). The adjacent angle is \(180 - 130=50^{\circ}\). If \(m\parallel n\), then \(200-2x = 50\) (corresponding angles).

Step2: Solve for \(x\)

Subtract \(200\) from both sides: \(-2x=50 - 200=-150\). Then \(x=\frac{-150}{-2}=75\).

Answer:

\(x = 3.75\)

Exercise 2