Question

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

Explanation:

Step1: Use property of parallel - sided figure

In a figure with parallel sides, the sum of adjacent angles is $180^{\circ}$. So, $(x + 50)+(3x + 20)=180$.

Step2: Solve the equation for x

Combine like - terms: $x+3x+50 + 20=180$, which simplifies to $4x+70 = 180$. Subtract 70 from both sides: $4x=180 - 70=110$. Then divide by 4: $x=\frac{110}{4}=15$.

Step3: Use another adjacent - angle relationship

The other pair of adjacent angles gives the equation $(2y - 5)+(x + 50)=180$. Substitute $x = 15$ into it: $(2y - 5)+(15 + 50)=180$.

Step4: Solve the equation for y

First simplify: $(2y - 5)+65 = 180$, then $2y+60 = 180$. Subtract 60 from both sides: $2y=180 - 60 = 120$. Divide by 2: $y = 50$.

Answer:

$x = 15$, $y = 50$