Question

Secants NE and SF intersect each other in the exterior of the circle

at the point M. If m(arc NS) = 125º, m(arc EF) = 37º, then m∠NMS =__.

(A) 33o

(B) 88o

(C) 22o

(D) 44o​

Answer 1

Answer:

NMS=88 degree

Step-by-step explanation:

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Answer 2

Answer:

The correct answer is option (D)

Step-by-step explanation:

Given,

Secants NE and SF intersect each other on the exterior of the circle.

m(arc NS) = 125º

m(arc EF) = 37º

Required to find,

m∠NMS

From the property of intersecting secants we have

When two secants intersect each other at the exterior of a circle, then the angle formed by the two secants is equal to half the difference between the measure of the intercepted arcs.

Here,

m∠NMS = $\frac{1}{2} (m(arc NS) - m(arc EF))$

= $\frac{1}{2} [125 -37]$

= $\frac{1}{2} X 88$

= 44°

Hence, m∠NMS = 44°

∴The correct answer is option(D)