Question

find the measure of ∠fli.
m∠fli =

Explanation:

Step1: Identify angle - relationship

Since $\angle FLI$ and $(7x + 21)^{\circ}$ are vertical - angles, they are equal. Also, $(7x + 21)^{\circ}$ and $(8x+69)^{\circ}$ are supplementary angles (linear pair), so $(7x + 21)+(8x + 69)=180$.

Step2: Solve the equation for x

Combine like - terms: $7x+8x+21 + 69=180$, which simplifies to $15x+90 = 180$. Subtract 90 from both sides: $15x=180 - 90=90$. Divide both sides by 15: $x=\frac{90}{15}=6$.

Step3: Find the measure of $\angle FLI$

Substitute $x = 6$ into the expression for the angle that is equal to $\angle FLI$ (the vertical - angle expression $7x + 21$). So $m\angle FLI=7x+21=7\times6 + 21$. Calculate $7\times6+21=42 + 21=63$.

Answer:

$63$