Question

in the adjoining figure, m (arcNS)=125° m (arcEF) =37°, Find the measure of angleNMS​

Answer 1

Answer:

We know, 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.

∴∠NMS=

2

1

[m(arcNS)—m(arcEF)]

⇒∠NMS=

2

1

×(125

o

−37

o

)=

2

1

×88

o

=44

o

Thus, the measure of ∠NMS is 44

o

.