What is the relation between ∠5 and the angle whose measure is 65^(∘)?
x=12
Practice makes perfect
Let's start by considering the given diagram.
Since ∠5 and the angle whose measure is 65^(∘) are both below the transversal and to the left of their respective lines, then they are corresponding angles. The lines being cut by the transversal are parallel. Therefore, according to the Corresponding Angles Theorem, corresponding angles are congruent.
m∠5= 65
We can also see that ∠5 and the angle whose measure is 11x-17 form a linear pair. According to the Linear Pair Postulate, these pair of angles are supplementary, which means that the sum of their measures is 180.
(11x-17)+m∠5=180
⇓
11x-17+65=180
Let's solve the equation for x.
