below are two parallel lines with a third line intersecting them.\nx = \\square ^\\circ
below are two parallel lines with a third line intersecting them.\nx = \\square ^\\circ
Answer
Explanation:
Step1: Identify angle relationship
The two lines are parallel, and the transversal creates same - side interior angles (or we can also consider the concept of supplementary angles for parallel lines cut by a transversal). The given angle is (116^{\circ}), and the angle (x) and the (116^{\circ}) angle are supplementary (they form a linear pair or are same - side interior angles which are supplementary when lines are parallel). The formula for supplementary angles is (a + b=180^{\circ}), where (a = 116^{\circ}) and (b=x).
Step2: Solve for (x)
Using the supplementary angle formula (x + 116^{\circ}=180^{\circ}). Subtract (116^{\circ}) from both sides: (x=180^{\circ}- 116^{\circ}). Calculate (180 - 116 = 64), so (x = 64^{\circ}).
Answer:
(64)