Question

Can you please help me out with a question

Answer 1

Notice that the arc GH has the same measure as the angle GFH, which also has the same measure as the angle EFI since they are vertical angles.

On the other hand, EFI and IFS are adjacent angles, then:

`m\angle EFI+m\angle IFS=m\angle EFS`

Observe that the measure of the angle EFS is 90°. Since the measure of IFS is 20°, substitute those values into the equation to find the measure of EFI:

`\begin{gathered} m\angle EFI+20=90 \\ \Rightarrow m\angle EFI=90-20 \\ \Rightarrow m\angle EFI=70 \end{gathered}`

Thereore, the measure of GH is 70°.