Question

15.) refer to the figure below.
a. find x so l || m.
b. using the value you found in part a, determine whether lines p and q are parallel.

Explanation:

Step1: Use corresponding - angles property

If \(l\parallel m\), then the corresponding angles are equal. So, \(3x + 5+(x - 5)=180\) (since they are same - side interior angles and for parallel lines, same - side interior angles are supplementary).

$$3x + 5+x - 5=180$$

Step2: Simplify the left - hand side

Combine like terms: \((3x+x)+(5 - 5)=180\), which gives \(4x=180\).

Step3: Solve for \(x\)

Divide both sides of the equation \(4x = 180\) by 4. So, \(x=\frac{180}{4}=45\).

Step4: For part b

Substitute \(x = 45\) into the angle measures related to lines \(p\) and \(q\). The angles formed by lines \(p\), \(q\) and the transversals are \(3x+5\) and \(45^{\circ}\). When \(x = 45\), \(3x+5=3\times45 + 5=135 + 5=140^{\circ}\). Since \(140^{\circ}
eq45^{\circ}\), lines \(p\) and \(q\) are not parallel.

Answer:

a. \(x = 45\)
b. Lines \(p\) and \(q\) are not parallel.