Question

in the diagram, (mangle fli) is (106^{circ}), (mangle flg=(2z - 1)^{circ}), (mangle glh=(z + 17)^{circ}), and (mangle hli=(4z - 15)^{circ}). what is the measure of the smallest angle in the diagram? (45^{circ}) (32^{circ}) (15^{circ}) (29^{circ})

Explanation:

Step1: Set up equation

$(2z - 1)+(z + 17)+(4z - 15)=106$

Step2: Combine like - terms

$7z + 1=106$

Step3: Solve for z

$7z=105$, so $z = 15$

Step4: Find angle measures

$m\angle FLG=2z - 1=2\times15 - 1 = 29^{\circ}$
$m\angle GLH=z + 17=15 + 17 = 32^{\circ}$
$m\angle HLI=4z - 15=4\times15 - 15 = 45^{\circ}$

Answer:

$29^{\circ}$