Question

Find the values of x and y if l || m.

Answer 1

`\begin{gathered} x=22 \\ y=15 \end{gathered}`

Step-by-step explanation

Step 1

when a lines intersects a pair of parallel lines , diverse angles are created

All angles that are either exterior angles, interior angles, alternate angles or corresponding angles are all congruent,so ( in the image yellow angles are corresponding, so)

`\begin{gathered} (5x+14)=(7x-30) \\ \end{gathered}`

solve for x

`\begin{gathered} (5x+14)=(7x-30) \\ \text{subtrac 5x in both sides} \\ (5x+14)-5x=(7x-30)-5x \\ 14=2x-30 \\ \text{add 30 in both sides} \\ 14+30=2x-30+30 \\ 44=2x \\ \text{divide both sides by 2} \\ (44)/(2)=(2x)/(2) \\ 22=x \end{gathered}`

Step 2

now, yellow angle and ble angles are supplementary( Two Angles are Supplementary when they add up to 180 degrees),so

`\begin{gathered} (3y+11)+(7x-30)=180 \\ \end{gathered}`

let

x=22

and solve for y

`\begin{gathered} (3y+11)+(7x-30)=180 \\ (3y+11)+(7\cdot22-30)=180 \\ (3y+11)+(7\cdot22-30)=180 \\ 3y+11+124=180 \\ 3y+135=180 \\ \text{subtract 135 in both sides} \\ 3y+135-135=180-135 \\ 3y=45 \\ \text{divide both sides by 3} \\ (3y)/(3)=(45)/(3) \\ y=15 \end{gathered}`

I hope this helps you