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प्रश्न
`square`MRPN is cyclic, ∠R = (5x – 13)°, ∠N = (4x + 4)°. Find measures of ∠R and ∠N.
उत्तर
`square`MRPN is cyclic. ...(Given)
∴ by theorem of cyclic quadrilateral,
∠R + ∠N = 180°
∴ (5x − 13)° + (4x + 4)° = 180°
∴ 5x − 13 + 4x + 4 = 180°
∴ 9x − 9 = 180
∴ 9x = 180 + 9
∴ 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°
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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`
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