In the figure, 0 is the centre
circle. ZPOQ=50°, then what is the measure
of arc PXQ and arc PYQ?

August 6, 2021

By Vivian

2 thoughts on “<br />In the figure, 0 is the centre<br />circle. ZPOQ=50°, then what is the measure<br />of arc PXQ and arc PYQ?<br /><br /><br /”

1. Step-by-step explanation:

   please send the picture of this question.

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2. Answer:

   100 degree

   Step-by-step explanation:

   We know, that radius is perpendicular to a tangent .

   ∴ ∠OPR=90

   o

   ⇒ ∠OPQ+∠QPR=90

   o

   ⇒ ∠OPQ+50

   o

   =90

   o

   ⇒ ∠OPQ=90

   o

   −50

   o

   ⇒ ∠OPQ=40

   o

   ⇒ OP=OQ [ Radii of a circle ]

   ⇒ ∠OPQ=∠OQP=40

   o

   [ Base angles of equal sides are also equal ]

   In △POQ,

   ⇒ ∠OQP+∠POQ+∠OPQ=180

   o

   [ Sum of angles of a triangle is 180

   o

   ]

   ⇒ 40

   o

   +∠POQ+40

   o

   =180

   o

   ⇒ ∠POQ+80=180

   o

   ⇒ ∠POQ=100

   o

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