Question

2
transversal \\( \overleftrightarrow { c d } \\) cuts parallel lines \\( \overleftrightarrow { p q } \\) and \\( \overleftrightarrow { r s } \\) at points \\( x \\) and \\( y \\) respectively. the point nearest to \\( c \\) is \\( x \\), and the point nearest to \\( d \\) is \\( y \\). \\( p \\) and \\( r \\) lie on one side of \\( \overleftrightarrow { c d } \\), while \\( q \\) and \\( s \\) lie on the other side. according to the alternate exterior angles theorem, which angle is congruent to \\( \angle c x p \\)?
\\( \bigcirc \\) a. \\( \angle r y d \\)
\\( \bigcirc \\) b. \\( \angle s y d \\)
\\( \bigcirc \\) c. \\( \angle c x q \\)
\\( \bigcirc \\) d. \\( \angle x y s \\)

Explanation:

The Alternate Exterior Angles Theorem states that when a transversal cuts two parallel lines, alternate exterior angles are congruent.

• For \(\angle CXP\), we need to find its alternate exterior angle.
• \(\overleftrightarrow{PQ}\parallel\overleftrightarrow{RS}\) and \(\overleftrightarrow{CD}\) is the transversal.
• \(\angle CXP\) and \(\angle SYD\) are on the exterior of the two parallel lines \(\overleftrightarrow{PQ}\) and \(\overleftrightarrow{RS}\) and on opposite sides of the transversal \(\overleftrightarrow{CD}\).

Answer:

B. \(\angle SYD\)