Question

in the given figure if <POR is110,then find the value of <PQR.

Answer 1

reflex <POR=360-110 degree

i.e. reflex<POR=250 degree

Therefore, <PQR= 250/2=125 degree

bcoz, < at center = 2 * < at perimeter.

Thank me only if you have understood it. THANK YOU

Answer 2

∠PQR = 125° if ∠POR = 110°

Step-by-step explanation:

∠POR = 110°

360° - ∠POR = 2 * ∠PQR

=> 360° - 110° = 2 * ∠PQR

=> 250°  = 2 * ∠PQR

=> ∠PQR = 125°

Another method

Take a point M on arc PR (arc other than arc arc PQR)

then PMRQ will be cyclic quadrilateral

∠PMR + ∠PQR = 180°

∠POR = 2∠PMR

=> 2∠PMR = 110°

=> ∠PMR = 55°

55° + ∠PQR = 180°

=> ∠PQR = 125°

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