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 \(\overleftrightarrow{PQ}\parallel\overleftrightarrow{RS}\) and \(\overleftrightarrow{CD}\) is a transversal, then \(\angle PXY\) and \(\angle XYS\) are consecutive interior angles.

Step2: Use the supplementary - angle formula

The formula for supplementary angles is \(m\angle PXY + m\angle XYS=180^{\circ}\). Given \(m\angle PXY = 64.36^{\circ}\).

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

Substitute the value of \(m\angle PXY\) into the formula: \(m\angle XYS=180^{\circ}-m\angle PXY\).

$$m\angle XYS = 180^{\circ}- 64.36^{\circ}=115.64^{\circ}$$

Answer:

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