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`

Answer 1

MRPN is a cyclic quadrilateral.   ...[Given]

Opposite angles of a cyclic quadrilateral are \[\boxed{\text{supplementary}}\].

∴ ∠R + ∠N = \[\boxed{180°}\]

∴ (5x – 13)° + (4x + 4)° = \[\boxed{180°}\]

∴ 9x – 9 = 180

∴ 9x = 189

∴ x = `189/9`

∴ x = 21

∴ ∠R = (5x – 13)°

∴ ∠R = (5 × 21 – 13)°

∴ ∠R = (105 – 13)°

∴ ∠R = \[\boxed{92°}\]

∴ ∠N = (4x + 4)°

∴ ∠N = (4 × 21 + 4)°

∴ ∠N = (84 + 4)°

∴ ∠N = \[\boxed{88°}\]

∴ m∠R = 92° and m ∠N = 88°