Question

solve for x.

x =
submit

Explanation:

Step1: Identify the relationship between angles

Since \(NO\parallel PQ\), \(\angle ORS\) and \(\angle QSR\) are same - side interior angles. Also, \(\angle NR L\) and \(\angle ORS\) are vertical angles. So \(\angle NR L=\angle ORS\). And \(\angle NR L+(3x + 5)^{\circ}=180^{\circ}\) (linear - pair of angles), \(\angle ORS\) and \(68^{\circ}\) are same - side interior angles. So \((3x + 5)+68=180\).

Step2: Solve the equation for \(x\)

Simplify the left - hand side of the equation \((3x + 5)+68=180\):

$$
LATEXBLOCK0
$$

Subtract \(73\) from both sides:

$$
LATEXBLOCK1
$$

Divide both sides by \(3\):

$$x=\frac{107}{3}\approx35.67$$

Wait, I made a mistake above. Actually, since \(NO\parallel PQ\), \(\angle NR L\) and \(68^{\circ}\) are corresponding angles. So \(3x + 5=68\)

Step2: Solve the correct equation for \(x\)

Subtract \(5\) from both sides of the equation \(3x + 5=68\):

$$
LATEXBLOCK2
$$

Divide both sides by \(3\):

$$x = 21$$

Answer:

\(x = 21\)