□MRPN is cyclic, ∠R = (5x-13)°, ∠N = (4x + 4)°. Find measures of ∠R and ∠N.
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✨✨R = 72°
N = 72°
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Step-by-step explanation:
Given that, MRPN is a cyclic quadrilateral.
In a cyclic quadrilateral opposite angles are equal.
So, R = N
R = 5x -13°
N = 4x + 4°
5x-13 = 4x+4
5x-4x = 4 + 13
x = 17° ✔️✔️✔️
R = 5x -13°= 5×17-13
= 72°
N = 4x + 4° = 4×17+4
= 72°
✔️✔️✔️
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#SOLUTION
MRPN is a cyclic quadrilateral.
∴ ∠R + ∠N = 180º (Opposite angles of a cyclic quadrilateral are supplementary)
⇒ 5x − 13º + 4x + 4º = 180º
⇒ 9x − 9º = 180º
⇒ 9x = 180º + 9º = 189º
⇒ x = 21º
∴ ∠R = 5x − 13º = 5 × 21º − 13º = 105º − 13º = 92º
∠N = 4x + 4º = 4 × 21º + 4º = 84º + 4º = 88º
Thus, the measures of ∠R and ∠N are 92º and 88º, respectively.
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