what is m∠g? m∠g = °

Explanation:

Step1: Use inscribed - angle theorem

In a circle, angles inscribed in the same arc are equal. So, $\angle G$ and $\angle E$ are inscribed in the same arc $\overset{\frown}{HF}$, and $\angle G=x + 40^{\circ}$, $\angle E=3x+2^{\circ}$. Then $x + 40^{\circ}=3x+2^{\circ}$.

Step2: Solve for $x$

Subtract $x$ from both sides: $40^{\circ}=2x + 2^{\circ}$. Then subtract $2^{\circ}$ from both sides: $38^{\circ}=2x$. Divide both sides by 2, we get $x = 19^{\circ}$.

Step3: Find $m\angle G$

Substitute $x = 19^{\circ}$ into the expression for $\angle G$. $m\angle G=x + 40^{\circ}=19^{\circ}+40^{\circ}=59^{\circ}$.

Answer:

$59$