Question

Quadrilateral mrpn is a cyclic angle r= (5x+13)degree,angle n=(4x+4)degree find meaasure of n and r

Answer 1

Correct Question :-

□MRPN is a cyclic quadrilateral, ∠R = (5x-13)° and ∠N=(4x+4)° then find measure of ∠R and ∠N.

To Find :-

• The measure of ∠R and ∠N.

Solution :-

Given,

• □ MRPN is cylic quadrilateral.
• ∠R = (5x - 13)°
• ∠N = (4x + 4)°

We know that,

The sum of either pair of opposite angles of a cylic quadrilateral is 180°.

⟹ ∠R + ∠N = 180°

⟹ (5x - 13)° + (4x + 4)° = 180°

⟹ 5x - 13 + 4x + 4 = 180°

⟹ 9x - 9 = 180°

⟹ 9x = 189

⟹ x = 21°

So,

• ∠R = (5x - 13)° = (5 × 21 - 13)° = (105 - 13)° = 92°.

• ∠N = (4x + 4) = (4 × 21 + 4)° = (84 + 4)° = 88°.

Therefore,

The measure of ∠R and ∠N is 92° and 88°.

Answer 2

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Quadrilateral mrpn is a cyclic angle r= (5x+13)degree,angle n=(4x+4)degree find meaasure of n and r

$</p><p>\large\overline{\underline{ \boxed{ \sf \red{\bigstar \: answer}}}}</p><p>$

$\bf \ \: In \: case \: of \: </h3><h3>cyclic \: quadrilateral \: opposite \: \\ \bf \: angles \: are \: supplimentary.$

$∠R+∠N= {180}^{o}$

$9x−9= {180}^{o}$

$x = {21}^{o}$

$∠R=5(21)−13 \\ =105−13 \\ = {92}^{o} </p><p></p><p>$

$∠N=4(21)+4 \\ = {88}^{o}$

$</p><p>\large\overline{\underline{ \boxed{ \sf {\ \: the \: values \: are \: {92}^{o} and \: {88}^{o} }}}}</p><p>$