Question

e
f
what is the value of y?
a 42
b 13
c 37
d 14

Explanation:

Step1: Use the property of same - side interior angles

Since lines \(e\) and \(f\) are parallel, the sum of \((9x + 12)^{\circ}\) and \((3x)^{\circ}\) is \(180^{\circ}\).
So, \(9x+12 + 3x=180\).
Combine like terms: \(12x+12 = 180\).
Subtract 12 from both sides: \(12x=180 - 12=168\).
Divide both sides by 12: \(x=\frac{168}{12}=14\).

Step2: Use the property of vertical angles

\((4y - 10)^{\circ}\) and \((3x)^{\circ}\) are vertical angles. So \(4y-10 = 3x\).
Substitute \(x = 14\) into the equation: \(4y-10=3\times14\).
Calculate \(3\times14 = 42\), then the equation becomes \(4y-10 = 42\).
Add 10 to both sides: \(4y=42 + 10=52\).
Divide both sides by 4: \(y=\frac{52}{4}=13\).

Answer:

B. 13