Question

find the measure of ∠loi. m∠loi =

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. $\angle LOI$ and $\angle KNH$ are vertical angles. So, $56 - 5x=52 - 3x$.

Step2: Solve the equation for x

Add $5x$ to both sides: $56=52 - 3x+5x$, which simplifies to $56 = 52+2x$. Then subtract 52 from both sides: $2x=56 - 52 = 4$. Divide both sides by 2: $x = 2$.

Step3: Find the measure of $\angle LOI$

Substitute $x = 2$ into the expression for $\angle LOI$. $\angle LOI=56-5x$. So, $\angle LOI=56-5\times2=56 - 10=46^{\circ}$.

Answer:

$46$