Question

solve for x.

x =

Explanation:

Step1: Use the property of corresponding angles

Since \( OP\parallel QR\), \(\angle MST\) and \(\angle QTN\) are corresponding angles. And \(\angle MST=(7x + 5)^{\circ}\), \(\angle QTN = 98^{\circ}\). Also, \(\angle MST\) and \((7x + 5)^{\circ}\) are vertical angles (vertical angles are equal). So \(7x+5=98\).

Step2: Solve the equation for \(x\)

Subtract \(5\) from both sides of the equation \(7x+5 = 98\):
\(7x=98 - 5\)
\(7x=93\)
Divide both sides by \(7\):
\(x=\frac{93}{7}\) (This is wrong. Wait, no, actually, \(\angle(7x + 5)\) and the angle adjacent to \(98^{\circ}\) (which is \(180 - 98=82^{\circ}\)) are corresponding angles. So \(7x+5=82\))

Correct Step1: Use the property of corresponding angles

Since \(OP\parallel QR\), \(\angle(7x + 5)\) and the angle adjacent to \(98^{\circ}\) (because they are corresponding angles). The adjacent angle of \(98^{\circ}\) is \(180-98 = 82^{\circ}\). So \(7x+5=82\)

Correct Step2: Solve the equation

Subtract \(5\) from both sides: \(7x=82 - 5=77\)
Divide both sides by \(7\): \(x = 11\)

Answer:

\(x = 11\)