Question

1. lines fg and jk are parallel, and mt is a transversal.

a. determine the value of p.
b. what is m∠fnt?
m∠fnt = 120°
c. what is m∠ktu?
m∠ktu = 70°

Explanation:

Step1: Use the property of corresponding - angles

Since lines FG and JK are parallel and MT is a transversal, the corresponding angles are equal. So, we set up the equation \(14p - 20=7p + 50\) because the angles \((14p - 20)^{\circ}\) and \((7p + 50)^{\circ}\) are corresponding angles.

Step2: Solve the equation for p

Subtract \(7p\) from both sides of the equation \(14p - 20=7p + 50\):
\(14p-7p - 20=7p-7p + 50\), which simplifies to \(7p-20 = 50\).
Then add 20 to both sides: \(7p-20 + 20=50 + 20\), getting \(7p=70\).
Divide both sides by 7: \(p = 10\).

Step3: Find the measure of \(\angle FNT\)

Substitute \(p = 10\) into the expression for the angle \((7p + 50)^{\circ}\).
\(m\angle FNT=7\times10 + 50=70 + 50=120^{\circ}\)

Step4: Find the measure of \(\angle KTU\)

Since \(\angle KTU\) and \(\angle FNT\) are vertical - angles, and vertical angles are equal, \(m\angle KTU = 120^{\circ}\)

Answer:

a. \(p = 10\)
b. \(m\angle FNT=120^{\circ}\)
c. \(m\angle KTU = 120^{\circ}\)