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प्रश्न
In a cyclic quadrilateral two adjacent angles are 40° and `pi^"c"/3`. Find the angles of the quadrilateral in degrees.
उत्तर
Let ABCD be the cyclic quadrilateral such that ∠A = 40° and ∠B = `pi^"c"/3`
= `(pi/3 xx 180/pi)^circ ...[because theta^"c" = (theta xx 180/pi)^circ]`
= 60°
∠A + ∠C = 180° ...`[("Opposite angles of a cyclic"),("quadrilateral are supplementary")]`
∴ 40° + ∠C = 180°
∴ ∠C = 180° – 40° = 140°
Also, ∠B + ∠D = 180° ....`[("Opposite angles of a cyclic"),("quadrilateral are supplementary")]`
∴ 60° + ∠D = 180°
∴ ∠D = 180° – 60° = 120°
∴ The angles of the quadrilateral in degrees are 40°, 60°, 140° and 120°.
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