Question

`square`MRPN is cyclic, ∠R = (5x – 13)°, ∠N = (4x + 4)°. Find measures of ∠R and ∠N.

Answer 1

`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°