Question

given m || n, find the value of x.
a) what type of angle pair is shown?
alternate interior
alternate exterior
same side interior
same side exterior
corresponding
linear pair
vertical
b) are the angles congruent or supplementary?
congruent(∠1 = ∠2)
supplementary(∠1 + ∠2 = 180°)
c) solve for x.
check your work. keep trying.
youve tried 6 times.

Explanation:

Step1: Identify angle - pair type

The angles are on opposite sides of the transversal and outside the parallel lines $m$ and $n$, so they are alternate - exterior angles.

Step2: Use angle - relationship property

Since alternate - exterior angles are congruent when two lines are parallel, we set up the equation $8x - 27=6x + 3$.

Step3: Solve the equation for $x$

Subtract $6x$ from both sides: $8x-6x - 27=6x - 6x+3$, which simplifies to $2x-27 = 3$.
Add 27 to both sides: $2x-27 + 27=3 + 27$, so $2x=30$.
Divide both sides by 2: $\frac{2x}{2}=\frac{30}{2}$, then $x = 15$.

Answer:

a) Alternate Exterior
b) Congruent
c) $x = 15$