Question

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

Answer 1

Answer:

Option C. $110\°$

Step-by-step 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

$m<AGC=\frac{1}{2}[81\°+59\°]$

$m<AGC=\frac{1}{2}[140\°]$

$m<AGC=70\°$

step 2

Determine the measure of angle FGC

we know that

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

so

$70\°+m<FGC=180\°$

$m<FGC=180\°-70\°=110\°$