WILL MARK BRIANLIEST
Find the measure of arc DF.

Circle A with chords EF and CD that intersect at point G, the measure of arc EC is 5x plus 10 degrees, the measure of angle EGC is 70 degrees, and the measure of arc DF is 11x plus 2 degrees.

50°
90°
100°
140°

  90°

Step-by-step explanation:

The measure of the given angle is the average of the measures of the intercepted arcs:

  70 = ((5x +10) +(11x +2))/2 = 8x +6

  (70 -6)/8 = x = 8

Then arc DF is ...

  11·8 +2 = 90 . . . . . degrees

Arc DF = 90°.

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Check

Arc CE is 5(8)+10 = 50 degrees, so the angle where the chords cross is (90+50)/2 = 70, as per the problem statement.

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