Question

In the given figure, O is the centre of the circle. PST IS
a straight line. If angle RST = 95°, then angle POR is equal to:
​

Answer 1

Answer:

Given: PST is a straight line

⇒ ∠RST+∠RSP=180°  (LINEAR PAIR)

⇒ ∠RSP=180°-∠RST

⇒ ∠RSP=180°- 95°

⇒ ∠RSP= 85°

We know that the angle subtended by an arc of a circle at its center is twice the angle subtended by the same arc at the circle circumference (on the same side of the arc/chord as the center).

⇒ 2∠RSP=∠POR

⇒ 2*85= ∠POR

⇒ 170°= ∠POR

STAN KPOP IDOLS

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Answer 2

Answer:

∠POR = 170°

Step-by-step explanation:

Let's join SO and produce it up to any arbitrary point x.

∠POX = ∠OPS + ∠OSP  [∠POX is exterior angle of ΔOPS]

Now ΔOPS is a isosceles triangle as OP = OS [radii of same circle]

∴ ∠OPS = ∠OSP

∴ ∠POX = 2∠OSP . . . . . . . . . . . . . . . (i)

By identical reasoning,

∠ROX = 2∠OSR . . . . . . . . . . . . . . . . (ii)

Adding equation (i) and (ii)

∠POR = 2∠PSR = 2 x (180° - 95°) = 2 x 85° = 170°