MN is the diameter of a circle with center O. P and S are two points on the circumference of the circle on either side of MN, such that ∠PMN = 50° and ∠MNS= 35°. What is the degree measure of the difference between ∠PMS and ∠PNS?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 30°.
We know that,
⇒ ∠MPN = 90° [Angle on semicircle]
In ΔPNM
⇒ ∠PNM = 90° - 50° = 40°
In the same way
⇒ ∠MSN = 90°
In ΔMSN
⇒ ∠SMN = 90° - 35° = 55°
So,
⇒ ∠PMS = ∠PMN + ∠NMS = 50° + 55° = 105°
⇒ ∠PNS = ∠PNM + ∠MNS = 35° + 40° = 75°
Required difference = 105° - 75° = 30°