Question

look at this diagram: if (overleftrightarrow{su}) and (overleftrightarrow{vx}) are parallel lines and (mangle vwt = 47.4^{circ}), what is (mangle utw)?

Explanation:

Step1: Use the property of parallel lines and transversal

When two parallel lines ($\overleftrightarrow{SU}$ and $\overleftrightarrow{VX}$) are cut by a transversal ($\overleftrightarrow{YR}$), consecutive - interior angles are supplementary. That is, $m\angle VWT+m\angle UTW = 180^{\circ}$.

Step2: Solve for $m\angle UTW$

We know that $m\angle VWT=47.4^{\circ}$. Substitute this value into the equation $m\angle VWT+m\angle UTW = 180^{\circ}$. Then $m\angle UTW=180^{\circ}-m\angle VWT$.

Substitute $m\angle VWT = 47.4^{\circ}$ into the formula:

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Answer:

$132.6$