Question

In the given figure, 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).

Answer 1

m(arc EF) = ∠ECF = 70º (Measure of an arc is the measure of its central angle)

Now,

m(arc DE) = 360º − m(arc EF) − m(arc DGF)

⇒ m(arc DE) = 360º − 70º − 200º = 90º

Also,

m(arc DEF) = m(arc DE) + m(arc EF)

⇒ m(arc DEF) = 90º + 70º = 160º

Thus, the m(arc DE) and m(arc DEF) is 90º and 160º, respectively.