Question

1 find the value of y. (14y - 4)° (3x + 11)° (x + 21)°

Explanation:

Step1: Find the value of \(x\)

Since \(2x + 11=x + 21\) (alternate - interior angles are equal for parallel lines).
Subtract \(x\) from both sides: \(2x-x+11=x - x+21\), so \(x+11 = 21\).
Subtract \(11\) from both sides: \(x=21 - 11=10\).

Step2: Find the value of \(y\)

\(14y-4\) and \(2x + 11\) are vertical angles. When \(x = 10\), \(2x+11=2\times10 + 11=31\).
So \(14y-4=31\).
Add \(4\) to both sides: \(14y-4 + 4=31+4\), so \(14y=35\).
Divide both sides by \(14\): \(y=\frac{35}{14}=\frac{5}{2}=2.5\).

Answer:

\(y = 2.5\)