Answer:
[tex]m\angle FOE=70^o[/tex]
[tex]m\angle GOH=55^o[/tex]
Step-by-step explanation:
We have been given an image of a circle and we are asked to find the [tex]m\angle FOE[/tex] and [tex]m\angle GOH[/tex].
We can see from our given circle that angle FOE is vertical angle of ZOH. Since the vertical angles are equal in measure, so measure of angle FOE will be equal to measure of angle ZOH.
We can see from our given diagram that [tex]m\angle ZOH=70^o[/tex], therefore, the measure of angle FOE will be equal to 70 degrees as well and option C is the correct choice.
Since the measure of angles on a circle is 360 degrees, so the measure of angle EOZ and FOH will be equal to 360 degrees minus 140 (2*70) degrees.
Since EOZ and FOH are vertical angles, so we can write the measure of both angles as:
[tex]2\times m\angle FOH=360^o-140^o[/tex]
[tex]2\times m\angle FOH=220^o[/tex]
Upon dividing both sides of our equation by 2 we will get,
[tex]\frac{2\times m\angle FOH}{2}=\frac{220^o}{2}[/tex]
[tex]m\angle FOH=110^o[/tex]
We can see from our given diagram that measure of angle GOH is equal to measure of angle GOF, so we can set an equation as:
[tex]m\angle GOH+m\angle GOF=m\angle FOH[/tex]
[tex]2\times m\angle GOH=m\angle FOH[/tex]
[tex]2\times m\angle GOH=110^o[/tex]
Upon dividing both sides of our equation by 2 we will get,
[tex]\frac{2\times m\angle GOH}{2}=\frac{110^o}{2}[/tex]
[tex]m\angle GOH=55^o[/tex]
Therefore, the measure of angle GOH is 55 degrees and option B is the correct choice.
