Question

given ( m parallel n ), find the value of ( x ) and ( y ).

Explanation:

Step1: Use the property of same - side interior angles

Since \(m\parallel n\), the sum of \((3x + 5)^{\circ}\) and \((8x+10)^{\circ}\) is \(180^{\circ}\) (same - side interior angles are supplementary).

$$3x + 5+8x + 10=180$$

$$11x+15 = 180$$

$$11x=180 - 15$$

$$11x=165$$

$$x = 15$$

Step2: Find the value of \(y\)

Substitute \(x = 15\) into \((3x + 5)^{\circ}\).
\(3x+5=3\times15 + 5=45 + 5=50\)
Since \(y\) and \((3x + 5)\) are alternate interior angles (because \(m\parallel n\)), \(y=3x + 5\)
So \(y = 50\)

Answer:

\(x = 15\), \(y = 50\)