Question

in the diagram, $m\angle fli$ is $106^\circ$, $m\angle flg = (2x - 1)^\circ$, $m\angle glh = (x + 17)^\circ$, and $m\angle hli = (4x - 15)^\circ$.
what is the measure of the smallest angle in the diagram?
$\bigcirc$ $15^\circ$
$\bigcirc$ $29^\circ$
$\bigcirc$ $32^\circ$
$\bigcirc$ $45^\circ$

Explanation:

Step1: Set up angle sum equation

The sum of the angles making up $\angle FLI$ equals $106^\circ$, so:
$$(2x-1)+(x+17)+(4x-15)=106$$

Step2: Simplify and solve for $x$

Combine like terms and isolate $x$:
$$7x + 1 = 106$$
$$7x = 105$$
$$x = 15$$

Step3: Calculate each angle

Substitute $x=15$ into each angle expression:

• $m\angle FLG = 2(15)-1 = 29^\circ$
• $m\angle GLH = 15+17 = 32^\circ$
• $m\angle HLI = 4(15)-15 = 45^\circ$

Step4: Identify the smallest angle

Compare the three calculated angles.

Answer:

29° (Option B)