Question

given m ∥ n, find the value of x and y. (4y-7)° (6x+9)° m (2x+3)° n

Explanation:

Step1: Use the property of corresponding angles

Since \(m\parallel n\), the corresponding angles \((6x + 9)^{\circ}\) and \((2x+3)^{\circ}\) are supplementary. So, \((6x + 9)+(2x + 3)=180\).
Simplify the left - hand side: \(6x+9 + 2x+3=8x + 12\).
Then the equation becomes \(8x+12 = 180\).
Subtract 12 from both sides: \(8x=180 - 12=168\).
Divide both sides by 8: \(x=\frac{168}{8}=21\).

Step2: Use the property of vertical angles

The angle \((4y - 7)^{\circ}\) and \((2x+3)^{\circ}\) are vertical angles. Substitute \(x = 21\) into \((2x+3)\): \(2x+3=2\times21 + 3=42 + 3=45\).
Since \(4y-7=45\).
Add 7 to both sides: \(4y=45 + 7=52\).
Divide both sides by 4: \(y=\frac{52}{4}=13\).

Answer:

\(x = 21\) and \(y = 13\)