Find each measure:

a) measure of arc eg (be sure to show all your work about how you arrived at your answer)

b) measure of arc de

(be sure to show all your work about how you arrived at your answer)

Angle DGH is 137/2 = 68.5, and angle HJG is 89. So we can find angle EHG as follows:
180 - (68.5 + 89)
= 180 - 157.5
= 22.5
Arc EG is twice 22.5, which is 45 degrees
Arc DE is 360 - (137 + 61 + 45), because the number of degrees in a circle is 360. We simplify as follows:
Arc DE = 117 degrees.
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Hope this helps!