Clockwise from top left, the 3 lines are labeled n, r, and s. Line n intersects both line r and

Question

In the figure, line $n$ intersects lines $r$ and $s$ . Line $r$ is parallel to line $s$ . What is the value of $x$ ?

Accepted Answer

The correct answer is 162 . It's given that line r is parallel to line s . Since line n intersects both lines r and s , it's a transversal. The angles in the figure marked as 162 &deg; and x &deg; are on the same side of the transversal, where one is an interior angle with line s as a side, and the other is an exterior angle with line r as a side. Thus, the marked angles are corresponding angles. When two parallel lines are intersected by a transversal, corresponding angles are congruent and, therefore, have equal measure. It follows that the value of x is 162 .

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