In the figure below, angle y and angle x form vertical angles. angle x forms a straight line with the 50° angle and the 40° angle.

write and solve an equation to determine the measure of angle y.

∠y = 90°

Step-by-step explanation:

Straight lines are all 180°.

If ∠x forms a straight line with the 40° and 50° angles:

∠x + 40° + 50° = 180°

Use this formula and isolate x.

∠x + 40° + 50° = 180°    Combine like terms (40° and 50°)

∠x + 90° = 180°    Subtract 90° from both sides to isolate x

∠x = 180° - 90°     Subtract

∠x = 90°

Since ∠x and ∠y are vertical angles, they have the same measure.

If ∠x = 90° and m∠x = m∠y, then ∠y = 90°.