Find the measure of ∠egc. circle a with chords ef and cd that intersect at point g, the measure of arc ec is 50 degrees, the measure of angle egc is 7x plus 7 degrees, and the measure of arc df is 10x degrees. 140° 90° 70° 50°

m∠EGC=70°

Step-by-step explanation:

we know that

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

so

m∠EGC=(1/2)[arc EC+arc DF]

Find the value of x

we have

m∠EGC=(7x+7)°

arc EC=50°

arc DF=10x°

substitute and solve for x

(7x+7)°=(1/2)[50°+10x°]

14x+14=50+10x

14x-10x=50-14

4x=36

x=9

Find the measure of angle EGC

m∠EGC=(7x+7)°

substitute the value of x

m∠EGC=(7(9)+7)°=70°