Question

Circle D is shown. Line segments E D, F D, and G D are radii. Angle E D F is 80 degrees and angle F D G is 35 degrees. Point H is on the other side of the circle.
Which equation can be used to find the measure of Arc E H G?

mArc E H G + 80 + 35 = 180
mArc E H G + 80 + 35 = 360
mArc E H G – 80 – 35 = 360
mArc E H G – 80 – 35 = 180

Answer 1

mArc EHG + 80 + 35 = 360

Reason: the small arc from E to G through F measures 80 + 35 = 115°, and the two arcs between E and G sum to 360°, so mArc EHG = 360 − 115 = 245°.