Question

find the measure of ∠fli. m∠fli =

Explanation:

Step1: Identify angle - relationship

Since $\angle FLI$ and $\angle JMK$ are corresponding angles (assuming $HI\parallel JK$), they are equal. Also, $\angle FLI=(5x - 3)^{\circ}$ and $\angle JMK=(147 - x)^{\circ}$.

Step2: Set up the equation

Set $5x-3 = 147 - x$.
Add $x$ to both sides: $5x+x-3=147 - x+x$, which simplifies to $6x-3 = 147$.
Add 3 to both sides: $6x-3 + 3=147+3$, so $6x=150$.
Divide both sides by 6: $x=\frac{150}{6}=25$.

Step3: Find the measure of $\angle FLI$

Substitute $x = 25$ into the expression for $\angle FLI$.
$\angle FLI=(5x - 3)^{\circ}=(5\times25-3)^{\circ}=(125 - 3)^{\circ}=122^{\circ}$.

Answer:

$122$