Question

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

Explanation:

Step1: Set up equation for \(x\)

Since \(m\parallel n\), the angles \((9x + 4)^{\circ}\) and \((7x+16)^{\circ}\) are equal (alternate - interior angles).

$$9x + 4=7x + 16$$

Subtract \(7x\) from both sides:

$$9x-7x + 4=7x-7x + 16$$

$$2x+4 = 16$$

Subtract \(4\) from both sides:

$$2x+4 - 4=16 - 4$$

$$2x=12$$

Divide both sides by \(2\):

$$x=\frac{12}{2}=6$$

Step2: Set up equation for \(y\)

The angles \((y + 3)^{\circ}\) and \((9x + 4)^{\circ}\) are supplementary (same - side interior angles).
First, substitute \(x = 6\) into \(9x + 4\): \(9\times6+4=54 + 4=58\)
Then, since \((y + 3)+(9x + 4)=180\) (supplementary angles), substitute \(9x + 4 = 58\)

$$y+3+58=180$$

$$y + 61=180$$

Subtract \(61\) from both sides:

$$y=180 - 61=119$$

Answer:

\(x = 6\) and \(y = 119\)