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

Question

In the figure shown, line $c$ intersects parallel lines $s$ and $t$ . What is the value of $x$ ?

Accepted Answer

The correct answer is 70 . Based on the figure, the angle with measure 110 /mo> and the angle vertical to the angle with measure x /mo> are same side interior angles. Since vertical angles are congruent, the angle vertical to the angle with measure x /mo> also has measure x /mo> . It&rsquo;s given that lines s and t are parallel. Therefore, same side interior angles between lines s and t are supplementary. It follows that x + 110 = 180 . Subtracting 110 from both sides of this equation yields x = 70 .

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