Question

given ( mparallel n ), find the value of x.
answer attempt 2 out of 2
( x=)

Explanation:

Step1: Use the property of alternate - exterior angles

Since \(m\parallel n\), the alternate - exterior angles are equal. So, \(3x + 7=x + 19+180\) (the \(180^{\circ}\) is because the angle adjacent to \((x + 19)^{\circ}\) forms a linear pair with the angle on line \(m\)).

Step2: Simplify the equation

\(3x+7=x + 199\).
Subtract \(x\) from both sides: \(3x - x+7=x - x + 199\), which gives \(2x+7 = 199\).

Step3: Solve for \(x\)

Subtract \(7\) from both sides: \(2x+7 - 7=199 - 7\), so \(2x=192\).
Divide both sides by \(2\): \(x=\frac{192}{2}=46\).

Answer:

\(x = 46\)