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 mea
sure of angle EGC is 7x plus 7 degrees, and the measure of arc DF is 10x degrees. 140° 90° 70° 50°
2 answers:
Answer:
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]
<u><em>Find the value of x</em></u>
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
<u><em>Find the measure of angle EGC</em></u>
m∠EGC=(7x+7)°
substitute the value of x
m∠EGC=(7(9)+7)°=70°
Answer:
C. 70
Step-by-step explanation:
Got it on my test.
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