Question

act prep practice! you must show complete work on your worksheet! answers that are only circled will not receive credit!
trapezoid dart with sides \\( \overline { d a } \parallel \overline { r t } \\) is shown below. if \\( \angle a \\) is \\( y ^ { \circ } \\), what is the degree measure of \\( \angle r \\) in terms of \\( y \\)?
\\( y ^ { \circ } \\)
\\( ( 180 - y ) ^ { \circ } \\)
\\( ( 180 - 0.5 y ) ^ { \circ } \\)
\\( ( 180 + 0.5 y ) ^ { \circ } \\)
\\( ( 180 + y ) ^ { \circ } \\)

Explanation:

Step1: Recall the property of consecutive interior angles

When two parallel lines are cut by a transversal, consecutive interior angles are supplementary. In trapezoid \(DART\) with \( \overline{DA}\parallel\overline{RT}\), \( \angle A\) and \( \angle R\) are consecutive interior angles.

Step2: Apply the supplementary - angle formula

If two angles \( \alpha\) and \( \beta\) are supplementary, then \( \alpha+\beta = 180^{\circ}\). Let \( \alpha=\angle A=y^{\circ}\) and \( \beta = \angle R\).
We have \(y+\angle R=180\).

Step3: Solve for \( \angle R\)

Subtract \(y\) from both sides of the equation \(y+\angle R = 180\).
\(\angle R=(180 - y)^{\circ}\)

Answer:

\((180 - y)^{\circ}\)