Question

(iii) In the figure,
m(arc NS) = 130°,
m(arc EF) = 60°
then find
(a) ZNMS
(b) ZENE
(c) ZNFS

​

Answer 1

Answer:

Hope it helps you friend

Answer 2

∠ ENF  = 30° , ∠ NFS  = 65° , ∠NMS = 35°

Step-by-step explanation:

m(arc NS) = 130°,

m(arc EF) = 60°

∠ ENF  = (1/2) ∠EOF  (angle subtended by chord at center = 2 * Angle subtended at Arc segment)

∠EOF  = m(arc EF) = 60°

=> ∠ ENF  = (1/2) 60°

=>  ∠ ENF  = 30°

∠ NFS  = (1/2) ∠NOS  

∠NOS  = m(arc NS) = 130°

=> ∠ NFS  = (1/2) 130°

=> ∠ NFS  = 65°

∠ NFS = ∠NMF  + ∠MNF  ( Exterio angle of triangle = Sum of opposite interior angles)

=> ∠ NFS =∠NMS + ∠ENF

=>   65° = ∠NMS + 30°

=> ∠NMS = 35°

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