Question

problem 15: find x and y. (first taught in lesson 24)

Explanation:

Step1: Use property of parallel - lines (alternate interior angles)

$3x + 20=x + 50$

Step2: Solve the equation for $x$

Subtract $x$ from both sides: $3x - x+20=x - x + 50$, $2x+20 = 50$. Then subtract 20 from both sides: $2x+20 - 20=50 - 20$, $2x = 30$. Divide both sides by 2: $x=\frac{30}{2}=15$.

Step3: Use property of parallel - lines (consecutive interior angles)

$(2y - 5)+(3x + 20)=180$

Step4: Substitute $x = 15$ into the equation

$(2y - 5)+(3\times15 + 20)=180$, $(2y - 5)+(45 + 20)=180$, $(2y - 5)+65 = 180$, $2y+60 = 180$.

Step5: Solve the equation for $y$

Subtract 60 from both sides: $2y+60 - 60=180 - 60$, $2y = 120$. Divide both sides by 2: $y=\frac{120}{2}=45$.

Answer:

$x = 15$, $y = 45$