In figure 3.37, points G, D, E, F are concyclic points of a circle with centre C. ECF = 70°, m(arc DGF) = 200° find m(arc DE) and m(arc DEF).


Given ECF = 70˚
m(arc DGF) = 200˚
m(arc EF) = 70˚ [The measure of a minor arc is the measure of its central angle.]
m(arc DGF)+m(arc EF)+m(arc DE) = 360˚ [Measure of a complete circle is 360°.]
200+70+ m(arc DE) = 360
m(arc DE) = 360-(200+70)
m(arc DE) = 90˚
m(arc DEF) = m(arc DE)+m(arc EF) [Property of sum of measures of arcs ]
m(arc DEF) = 90+70
m(arc DEF) = 160˚

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