The measurement of Đ PQR is
P
a
R
0
280
360
(int) 160
(iv) 260​

Question

The measurement of Đ PQR is
P
a
R
0
280
360
(int) 160
(iv) 260​

in progress 0
Valentina 2 years 2021-07-08T04:03:12+00:00 1 Answers 0 views 0

Answers ( )

    0
    2021-07-08T04:04:17+00:00

    Answer:

    We know angle subtended at centre by an arc is double the angle subtendedby it at any other point.

    Reflex angle ∠POR= 2∠PQR

    = 2 × 100°

    = 200°

    Now, ∠POR = 360° – 200 = 160°

    Also,

    PO = OR [Radii of a circle]

    ∠OPR = ∠ORP [Opposite angles of isosceles triangle]

    In ∆OPR, ∠POR = 160°

    ∴ ∠OPR = ∠ORP = 10°

    Method 2:

    Consider PR as a chord of the circle. Take any point S on the major arc of the circle

    PQRS is a cyclic quadrilateral

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