Question

1. the figure shown is not drawn to scale. find the values of x and y so that the lines shown are parallel. x = 50 y = 130 3x - 130 20 = 8x - 130 + 130 50

Explanation:

Step1: Use corresponding - angles property

For the parallel lines, the corresponding angles are equal. We have the equation based on the corresponding - angles: $x + 10=50$.

Step2: Solve for $x$

Subtract 10 from both sides of the equation $x + 10=50$. So, $x=50 - 10=40$.

Step3: Use linear - pair property

The angle $(y - 140)^{\circ}$ and the angle $(y + 20)^{\circ}$ form a linear - pair. So, $(y - 140)+(y + 20)=180$.

Step4: Simplify the equation for $y$

Expand the left - hand side: $y-140 + y+20=180$. Combine like terms: $2y-120 = 180$.

Step5: Solve for $y$

Add 120 to both sides: $2y=180 + 120=300$. Divide both sides by 2: $y = 150$.

Answer:

$x = 40$, $y = 150$