What is the relation between ∠4 and the angle whose measure is 118^(∘)?
x=7
Practice makes perfect
Let's start by considering the given diagram.
We see that ∠4 and the angle whose measure is 118^(∘) form a linear pair. Therefore, according to the Linear Pair Postulate, they are supplementary angles and the sum of their measures is 180.
m∠4+ 118 = 180 ⇔ m∠4 = 62
Moreover, we also see in the figure that ∠4 and the angle whose measure is (8x+6)^(∘) are alternate interior angles. Since the lines being cut by the transversal are parallel, according to the Alternate Interior Angles Theorem, these angles are congruent and hence they have the same measure.
8x+6=m∠4
⇓
8x+6=62
Let's solve the equation for x.
