Find the measure of arc EC.

Circle A with chords EF and CD that intersect at point G, the measure of arc EC is 5x degrees, the measure of angle EGC is 7x degrees, and the measure of arc DF is 90 degrees.

The exterior angle of a polygon is the angle of rotation between one extended side and its neighboring side, which is not extended.

Furthermore, because the polygon is regular, even though it has 'n' sides, all the outside angles have the same measure, and hence their measure is (360/n)°.

The measure of arc EC is found as;

[tex]\rm 7x = (90+5x)\times \frac{1}{2}\\\\ 7x=2.5x+45\\\\ 4.5 x=45 \\\\ x=10[/tex]

From the diagram,he EC is 5x . The measure of arc EC is;

EC=5x

EC=5×10

EC=50

Hence,the measure of arc EC will be 50.

Learn more about interior and exterior angles refer:

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Find the measure of arc EC. Circle A with chords EF and CD that intersect at point G, the measure of arc EC is 5x degrees, the measure of angle EGC is 7x degrees, and the measure of arc DF is 90 degrees.

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Find the measure of arc EC.

Circle A with chords EF and CD that intersect at point G, the measure of arc EC is 5x degrees, the measure of angle EGC is 7x degrees, and the measure of arc DF is 90 degrees.