Question

In the figure,
m(arc NS) = 130°,
m(arc EF) = 60°
then find
(a) NMS
(b) ENF
(c) NFS​

Answer 1

(a) ∠ NMS = 35°

(b) ∠ ENF = 60°

(c) ∠ NFS = 130°

Step-by-step explanation:

Given:

Here, m(arc NS) = 130°,  m(arc EF) = 60°

(a) As all of us know that if two lines containing chords of a circle intersect each other outside the circle, then the measure of the angle between them is half the difference in measures of the arcs intercepted by the angle.

So $\angle NMS = \frac{1}{2}[m(arc NS) - m(arc EF) ]$

⇒ $\angle NMS = \frac{1}{2}[130-60]$

⇒ $\angle NMS = \frac{1}{2}[70]$

⇒ ∠ NMS = 35°

Also we know that, measure of an angle is equal to its arc opposite arc.

So,

(b) ∠ ENF =  m(arc EF)

⇒ ∠ ENF = 60°                                   [given]

(c) ∠ NFS​ = m(arc NS)

⇒ ∠ NFS = 130°                                  [given]

Answer 2

Answer:

Hope it helps you friend

Step-by-step explanation: