Question

look at this diagram:
if (overleftrightarrow{ik}) and (overleftrightarrow{ln}) are parallel lines and (mangle ijm = 140^{circ}), what is (mangle kjm)?

Explanation:

Step1: Use the property of supplementary angles

Supplementary angles sum to \(180^{\circ}\). Given \(m\angle IJM = 140^{\circ}\), and \(\angle IJM\) and \(\angle KJM\) are supplementary.
Let \(m\angle KJM=x\). Then the equation is \(x + 140^{\circ}=180^{\circ}\).

Step2: Solve the equation for \(x\)

Subtract \(140^{\circ}\) from both sides of the equation \(x+140^{\circ}=180^{\circ}\).
\(x=180^{\circ}- 140^{\circ}\)
\(x = 40^{\circ}\)

Answer:

\(40\)