Question

select the correct answer.

transversal \\( \overleftrightarrow { c d } \\) cuts parallel lines \\( \overleftrightarrow { p q } \\) and \\( \overleftrightarrow { r s } \\) at points \\( x \\) and \\( y \\), respectively. points \\( p \\) and \\( r \\) lie on one side of \\( \overleftrightarrow { c d } \\), while \\( q \\) and \\( s \\) lie on the other side. if \\( m \angle p x y = 64.36 ^ { \circ } \\), what is \\( m \angle x y s \\)?

\\( \bigcirc \\) a. \\( 180 ^ { \circ } \\)
\\( \bigcirc \\) b. \\( 115.64 ^ { \circ } \\)
\\( \bigcirc \\) c. \\( 64.36 ^ { \circ } \\)
\\( \bigcirc \\) d. \\( 25.64 ^ { \circ } \\)

Explanation:

Step1: Recall the property of consecutive interior angles

When a transversal cuts two parallel lines, consecutive interior angles are supplementary. That is, if two parallel lines \( \overleftrightarrow{PQ}\) and \( \overleftrightarrow{RS}\) are cut by a transversal \( \overleftrightarrow{CD}\), then \(m\angle PXY + m\angle XYS=180^{\circ}\).

Step2: Solve for \(m\angle XYS\)

We know that \(m\angle PXY = 64.36^{\circ}\). Using the equation \(m\angle XYS=180^{\circ}-m\angle PXY\), substitute the value of \(m\angle PXY\):
\(m\angle XYS = 180^{\circ}- 64.36^{\circ}\)
\(m\angle XYS=115.64^{\circ}\)

Answer:

B. \(115.64^{\circ}\)