Question

꯳MRPN is cyclic, ∠R=(5x-13)°, ∠N=(4x+4)°. Find measures of ∠R and ∠N.

Answer 1

In case of the cyclic quadrilateral, Opposite angles are supplementary. 

∴ ∠R + ∠N = 180°
⇒ 5x - 13 + 4x + 4 = 180
⇒ 9x - 9 = 180
⇒ x - 1 = 20
∴ x = 21

Now, 
∠ R = 5x - 13 = 5(21) - 21
= 105 - 21
= 84°

∠N = 4x + 4 = 8(21) + 4
= 84 + 4
= 88°


Hope it helps.

Answer 2

SOLUTION:-
GIVEN BY :- quadrilateral (MNPN ) CYCLIC
THEN,
∠R + ∠N = 180°,
=>( 5x-13) + (4x+4) = 180
=> 9x = 180+9
=> x = 189/9
=> x = 21
we get,
∠R = (5x-13)
= (5×21-13)
= 105-13
= 92°,
*******************
∠N=(4x+4)°
= (21×4 +4 )
= ( 84 +4)
= 88°.

(∠R ,∠N ) = ( 92°, 88°)
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