Question

find the measure of ∠eki.
(5x - 4)°
(3x - 8)°
m∠eki = □°

Explanation:

Step1: Identify angle - relationship

Since the two vertical lines are parallel, the angles $(3x - 8)^{\circ}$ and $(5x - 4)^{\circ}$ are corresponding angles and are equal.
$3x-8 = 5x - 4$

Step2: Solve for x

Subtract $3x$ from both sides:
$-8=2x - 4$
Add 4 to both sides:
$- 4=2x$
Divide both sides by 2:
$x=-2$

Step3: Find the measure of $\angle EKI$

Substitute $x = - 2$ into the expression for $\angle EKI=(5x - 4)^{\circ}$
$m\angle EKI=5\times(-2)-4$
$m\angle EKI=-10 - 4=-14$ (This is incorrect. We made a wrong - start. The angles are actually alternate interior angles)

Let's start over:
Since the two vertical lines are parallel, the angles $(3x - 8)^{\circ}$ and $(5x - 4)^{\circ}$ are alternate interior angles and are equal.
$3x-8 = 5x - 4$
Subtract $3x$ from both sides:
$-8 = 2x-4$
Add 4 to both sides:
$-4=2x$
$x=-2$ (This is wrong. Let's correct the equation. They are same - side interior angles, so $(3x - 8)+(5x - 4)=180$)

Step1: Set up the correct equation

Since the two vertical lines are parallel, the angles $(3x - 8)^{\circ}$ and $(5x - 4)^{\circ}$ are same - side interior angles. So, $(3x - 8)+(5x - 4)=180$
Combine like terms:
$3x+5x-8 - 4=180$
$8x-12 = 180$

Step2: Solve for x

Add 12 to both sides:
$8x=192$
Divide both sides by 8:
$x = 24$

Step3: Find the measure of $\angle EKI$

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

Answer:

$116$