Question

What is the measure of arc EF in circle H?
O 41°
O 50°
O 114
O 1730

Answer 1

41

Explanation:

answer is 41

Answer 2

The measure of arc EF = 41°

Explanation:

Given:

Arc DE = 73°

`\angle FED=123\°`

Now, we know from central angle theorem that the measure of central angle by an arc is twice that of the angle made by the same arc at the circumference. Therefore,

`\textrm{Major Arc DGF}=2* \angle FED\\\textrm{Major Arc DGF}=2* 123\\\textrm{Major Arc DGF}=246\°`

Now, we know that sum of all arcs on a circle is equal to 360°.

Therefore, arc DGF + arc DE + arc EF = 360°

`246+73+arc\ EF=360\\319+arc\ EF=360\\arc\ EF=360-319=41\°`

Therefore, the measure of the arc EF is 41°.