We are given three parallel lines, all of which are intersected by a transversal. When this occurs, angle relationships are formed.
Notice the angle measure at the intersection of line n and the transversal is 133°. Now, notice the angle measure at the intersection of the transversal and line l; the measure is Algebraically (7x+7)°. Now, ask yourself: what do the location of these two angles have in common? The answer is that they are corresponding angle pairs, since they are in the same position but on different lines (different locations). What do we know about corresponding angles? Well, there is a theorem that states that corresponding angles are congruent; this is the Corresponding Angles Theorem.
So, we know the two angles are corresponding angles, and according to this theorem, the angle measures are congruent. This means the angles are equal to each other, so we can form an equation and solve for “x:”
(7x+7)°=133°
All we have done so far is set the angles equal to each other because corresponding angles (angles in the same position but different location) are congruent. So, (7x+7)° must be equal to 133°. We need to solve for a variable “x,” which would make the expression equal to 133°.
Let’s solve for “x:”
(7x+7)=133
Combine like terms: subtract 7 from both sides:
7x=133-7
7x=126
Divide both sides by 7:
x=126/7
x=18
So, let’s check if this creates a true statement when x=18:
7(18)+7=133
126+7=133
133=133
So, the answer is x=18