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

Question

In the figure, line $q$ is parallel to line $r$ , and both lines are intersected by line $s$ . If $y = 2 x + 8$ , what is the value of $x$ ?

Accepted Answer

The correct answer is 57 . Based on the figure, the angle with measure y &#176; and the angle vertical to the angle with measure 58 &#176; are same side interior angles. Since vertical angles are congruent, the angle vertical to the angle with measure 58 &#176; also has measure 58 &#176; . It&rsquo;s given that lines q and r are parallel. Therefore, same side interior angles between lines q and r are supplementary. It follows that y + 58 = 180 . If y = 2 x + 8 , then the value of x can be found by substituting 2 x + 8 for y in the equation y + 58 = 180 , which yields 2 x + 8 + 58 = 180 , or 2 x + 66 = 180 . Subtracting 66 from both sides of this equation yields 2 x = 114 . Dividing both sides of this equation by 2 yields x = 57 . Thus, if y = 2 x + 8 , the value of x is 57 .

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