The angle at the intersection of line n is 54°. Since lines l, m, and n are parallel lines intersected by a transversal, the angle at the intersection of the transversal and line n, measured 54°, is a vertical angle of the opposite angle. Because of this, the angle vertically opposite of the 54° angle, is congruent to 54°, according to the Vertical Angles Theorem.
This forms a pair of same-side interior angles. If we recall the same-side interior angles theorem, we know that that these two angles are supplementary. Supplementary means that the sum of the two angles is 180.°
So, let’s create an Algebraic equation using this theorem:
(2x+20)°+54°=180°
Now, let’s solve for “x” algebraically:
Subtract 54 from both sides:
2x+20=180-54
2x+20=126
Subtract 20 from both sides:
2x=126-20
2x=106
Divide both sides by 2:
x=106/2
x=53
Let’s check this in the original equation:
(2(53)+20)°+54°=180°
(106+20)°+54°=180°
126°+54°=180°
180°=180°
So, your answer is x=53