Question

Ratio of measures of PQRS is 7:9:3:5 then find the measures of its angles and write
the type of quadrilateral.​

Answer 1

Given : Ratio of measures of angle in a quadrilateral is 7:9:3:5 respectively

To Find : The measurements of the angles

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❒ Let the angles in the quadrilateral be denoted as 7x , 9x , 3x and 5x

${ \underline{ \frak{ \dag \: As \: we \: know \: that : }}}$

$\: \: \: \: \: \: \dag \: \bigg[ \bf \: sum \: of \: interior \: angles _{(quadrilateral)} = 360 \degree \bigg]$

★ Here, interior angles are :

• 7x
• 9x
• 3x
• 5x

${ \underline{ \bf{ \bigstar \: Framing \: an \: equation \: we \: get : }}}$

${ : \implies} \sf \: 7x + 9x + 5x + 3x = 360 \degree \\ \\ \\ { : \implies} \sf \: 16x + 5x + 3x = 360 \degree \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \sf \: 16x + 8x = 360 \degree \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \sf \: 24x = 360 \degree \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \sf \: x = \frac{360}{24} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies}{ \pink{ \boxed{ \frak{x = 15}} \star}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

${ \underline{ \frak{ now \: let \: us \: find \: the \: angles : }}}$

$\\{ \purple{ \mapsto}} \tt \: 7x = 7(15) = 105 \degree \\ \\ { \purple{ \mapsto}} \tt \: 9x = 9(15) = 135 \degree \\ \\ { \purple{ \mapsto}} \tt \: 3x = 3(15) = 45 \degree \: \: \\ \\ { \purple{ \mapsto}} \tt \: 5x = 5(15) = 75 \degree$

${\underline{\rm{\therefore the\: anlges \: are\: 105,135,45,75 \: degrees \:respectively}}}$

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