Question

find the measure of ∠loi.
k (5x + 19)°
(9x - 5)°
m∠loi =
submit

Explanation:

Step1: Identify vertical - angle relationship

Since vertical angles are equal, $\angle KNH$ and $\angle LOI$ are vertical angles. So $5x + 19=9x - 5$.

Step2: Solve the equation for $x$

Subtract $5x$ from both sides: $19 = 9x-5 - 5x$, which simplifies to $19 = 4x-5$.
Add 5 to both sides: $19 + 5=4x$, so $24 = 4x$.
Divide both sides by 4: $x=\frac{24}{4}=6$.

Step3: Find the measure of $\angle LOI$

Substitute $x = 6$ into the expression for $\angle LOI$: $m\angle LOI=9x - 5$.
$m\angle LOI=9\times6 - 5=54 - 5 = 49$.

Answer:

$49$