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°

Accepted Solution

Answer:m∠EGC=70°Step-by-step explanation:we know thatThe measure of the inner angle is the semi-sum of the arcs comprising it and its oppositesom∠EGC=(1/2)[arc EC+arc DF]Find the value of xwe havem∠EGC=(7x+7)°arc EC=50°arc DF=10x°substitute and solve for x(7x+7)°=(1/2)[50°+10x°]14x+14=50+10x14x-10x=50-144x=36x=9Find the measure of angle EGCm∠EGC=(7x+7)°substitute the value of xm∠EGC=(7(9)+7)°=70°