Question

look at this diagram: if $overleftrightarrow{su}$ and $overleftrightarrow{vx}$ are parallel lines and $mangle utr = 49^{circ}$, what is $mangle utw$?

Explanation:

Step1: Recall linear - pair property

Linear - pair of angles are supplementary, i.e., their sum is 180°. ∠UTR and ∠UTW form a linear - pair.

Step2: Set up the equation

Let \(m\angle UTR = 49^{\circ}\) and \(m\angle UTR+m\angle UTW = 180^{\circ}\).

Step3: Solve for \(m\angle UTW\)

\(m\angle UTW=180^{\circ}-m\angle UTR\). Substitute \(m\angle UTR = 49^{\circ}\) into the equation: \(m\angle UTW = 180 - 49=131^{\circ}\).

Answer:

131