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Question
MRPN is cyclic, ∠R = (5x – 13)°, ∠N = (4x + 4)°. Find measures of ∠R and ∠N, by completing the following activity.
Solution:
MRPN is cyclic
The opposite angles of a cyclic square are `square`
∠R + ∠N = `square`
∴ (5x – 13)° + (4x + 4)° = `square`
∴ 9x = 189°
∴ x = `square`
∴ ∠R = (5x – 13)° = `square`
∴ ∠N = (4x + 4)° = `square`
Solution
MRPN is a cyclic quadrilateral. ......[Given]
Opposite angles of a cyclic quadrilateral are supplementary.
∴ ∠R + ∠N = 180°
∴ (5x – 13)° + (4x + 4) ° = 180°
∴ 9x − 9 = 180
∴ 9x = 189
∴ x = `189/9`
∴ x = 21
∴ ∠R = (5x – 13)°
∴ ∠R = (5 × 21 − 13)°
∴ ∠R = (105 − 13)°
∴ ∠R = 92°
∴ ∠N = (4x + 4)°
∴ ∠N = (4 × 21 + 4)°
∴ ∠N = (84 + 4)°
∴ ∠N = 88°
∴ m∠R = 92° and m ∠N = 88°
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