Question

find the measure of ∠eki.
(3x - 8)°
(5x - 4)°
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.
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Explanation:

Step1: Identify angle - pair type

The angles $(3x - 8)^{\circ}$ and $(5x - 4)^{\circ}$ are same - side interior angles as they are on the same side of the transversal and between the two parallel lines.

Step2: Determine angle relationship

Same - side interior angles are supplementary, so $(3x - 8)+(5x - 4)=180$.

Step3: Simplify the equation

Combine like terms: $3x+5x-8 - 4 = 180$, which gives $8x-12 = 180$.

Step4: Solve for x

Add 12 to both sides: $8x=180 + 12=192$. Then divide both sides by 8: $x=\frac{192}{8}=24$.

Step5: Find the measure of $\angle EKI$

Substitute $x = 24$ into the expression for $\angle EKI=(5x - 4)^{\circ}$. So $\angle EKI=5\times24-4=120 - 4 = 116^{\circ}$.

Answer:

a) Same Side Interior
b) Supplementary$(\angle1+\angle2 = 180^{\circ})$
c) $x = 24$