Question

two parallel lines are crossed by a transversal. what is the value of y? o y = 40 o y = 80 o y = 100 o y = 120

Explanation:

Step1: Identify angle - relationship

When two parallel lines are cut by a transversal, the given $80^{\circ}$ angle and the angle adjacent to $y^{\circ}$ are corresponding angles. Corresponding angles are equal. So the angle adjacent to $y^{\circ}$ is $80^{\circ}$.

Step2: Use linear - pair property

The $80^{\circ}$ angle and $y^{\circ}$ form a linear - pair. The sum of angles in a linear - pair is $180^{\circ}$. So we have the equation $y + 80=180$.

Step3: Solve for $y$

Subtract $80$ from both sides of the equation: $y=180 - 80$.
$y = 100$

Answer:

$y = 100$, so the correct option is C. $y = 100$