Question

find the measure of ∠ilf.
(6x - 5)°
(5x - 2)°
m∠ilf = □°

Explanation:

Step1: Identify vertical - angle relationship

Vertical angles are equal. $\angle EKG$ and $\angle ILF$ are vertical angles, so $6x - 5=5x - 2$.

Step2: Solve the equation for $x$

Subtract $5x$ from both sides: $6x-5x - 5=5x-5x - 2$, which simplifies to $x - 5=-2$. Then add 5 to both sides: $x=-2 + 5$, so $x = 3$.

Step3: Find the measure of $\angle ILF$

Substitute $x = 3$ into the expression for $\angle ILF$ which is $5x-2$. So $m\angle ILF=5\times3-2=15 - 2=13$.

Answer:

$13$