Question

1. (mangle hgf = 16x + 4), (mangle egf=110^{circ}), and (mangle hge = 3x + 11). find (x).

Explanation:

Step1: Use angle - addition postulate

Since $\angle HGF=\angle HGE+\angle EGF$, we can write the equation $16x + 4=(3x + 11)+110$.

Step2: Simplify the right - hand side of the equation

$16x + 4=3x+121$.

Step3: Subtract $3x$ from both sides

$16x-3x + 4=3x-3x + 121$, which gives $13x+4 = 121$.

Step4: Subtract 4 from both sides

$13x+4 - 4=121 - 4$, so $13x=117$.

Step5: Divide both sides by 13

$\frac{13x}{13}=\frac{117}{13}$, then $x = 9$.

Answer:

$x = 9$