Question

Determine the measure of angle FGC.
A. 22°
B. 70°
C. 110°
D.120°

Answer 1

Option C.
`110\°`

Explanation:

step 1

Determine the measure of angle AGC

we know that

The measure of the inner angle is the semi-sum of the arcs comprising it and its opposite.

so

`m<AGC=(1)/(2)[81\°+59\°]`

`m<AGC=(1)/(2)[140\°]`

`m<AGC=70\°`

step 2

Determine the measure of angle FGC

we know that

`m<AGC+m<FGC=180\°` ----> by supplementary angles

so

`70\°+m<FGC=180\°`

`m<FGC=180\°-70\°=110\°`