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Geometry and Trigonometry / Lines, angles, and triangles Difficulty: Easy

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

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Explanation

The correct answer is $70$ . Based on the figure, the angle with measure $110 degree$ and the angle vertical to the angle with measure $x °$ are same side interior angles. Since vertical angles are congruent, the angle vertical to the angle with measure $x °$ also has measure $x °$ . It’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 $x equals 70$ .