which arc is congruent to $widehat{eh}$?\n$\bigcirc widehat{gh}$\n$\bigcirc widehat{fh}$\n$\bigcirc…
which arc is congruent to $widehat{eh}$?\n$\bigcirc widehat{gh}$\n$\bigcirc widehat{fh}$\n$\bigcirc widehat{ge}$\n$\bigcirc widehat{fg}$
Answer
Answer:
C. $\widehat{GE}$
Explanation:
Step1: Recall congruent - arc property
In a circle, two arcs are congruent if they have the same measure.
Step2: Calculate measure of $\widehat{EH}$
The measure of $\widehat{EH}$ is $110^{\circ}$.
Step3: Calculate measure of each arc
- Measure of $\widehat{GH}=70^{\circ}$.
- Measure of $\widehat{FH}=55^{\circ}+70^{\circ}=125^{\circ}$.
- Measure of $\widehat{GE}=110^{\circ}$ (since the central - angle corresponding to $\widehat{GE}$ is $110^{\circ}$).
- Measure of $\widehat{FG}=55^{\circ}$. So, the arc congruent to $\widehat{EH}$ is $\widehat{GE}$.