Question

which arc is congruent to $widehat{eh}$?$\bigcirc$ $widehat{gh}LXB0\bigcirc$ $widehat{ge}$$\bigcirc$ $widehat{fg}$

Explanation:

Step1: Calculate arc $\widehat{EH}$ measure

The central angle for $\widehat{EH}$ is supplementary to the $55^\circ$ angle on straight line $FH$.
$\text{Measure of } \widehat{EH} = 180^\circ - 55^\circ = 125^\circ$

Step2: Calculate arc $\widehat{FG}$ measure

The central angle for $\widehat{FG}$ is supplementary to the $110^\circ$ angle on straight line $FH$.
$\text{Measure of } \widehat{FG} = 180^\circ - 110^\circ = 70^\circ$ (correction: calculate remaining arc for $\widehat{FG}$: total circle $360^\circ$, subtract known arcs: $360^\circ - 55^\circ - 125^\circ - 70^\circ = 110^\circ$? No, correct: central angle for $\widehat{EH}$: $360 - 55 -70 -110 = 125^\circ$. Central angle for $\widehat{FG}$ is $70^\circ$? No, wait: $\widehat{EH}$ central angle is $125^\circ$. Now calculate $\widehat{GE}$: $360 - 55 -70 -110 = 125^\circ$. Yes, $\widehat{GE}$ central angle is $125^\circ$, same as $\widehat{EH}$.

Step3: Match congruent arcs

Congruent arcs have equal central angles. $\widehat{EH}$ and $\widehat{GE}$ both have $125^\circ$ central angles.

Answer:

$\boldsymbol{\overline{GE}}$