Question

2. The angles P,Q,R and Sare in the ratio 1:3:7:9. Find the measure of all angles a customer for Rs 1504​

Answer 1

Answer:

Given ratio of angles of quadrilateral PQRS is 1:3:7:9

Let the angles of quadrilateral PQRS be x,3x,7x,9x, respectively.

$</p><p> .⇒∠P+∠Q+∠R+∠S=360 </p><p></p><p> °</p><p></p><p>⇒x+3x+7x+9x=360 </p><p>°</p><p> </p><p></p><p>⇒20x=360 </p><p>°</p><p> </p><p></p><p>⇒x= </p><p>20</p><p>360 </p><p>°</p><p> </p><p> </p><p> </p><p></p><p>∴x=18 </p><p>°</p><p> .</p><p></p><p></p><p></p><p>∴∠P=x=18 </p><p>°</p><p> ,</p><p></p><p>∠Q=3x=3×18 </p><p>°</p><p> =54 </p><p>°</p><p> ,</p><p></p><p>∠R=7x=7×18 </p><p>°</p><p> =126 </p><p>°</p><p> </p><p></p><p>and ∠S=9x=9×18 </p><p>°</p><p> =162 °</p><p></p><p></p><p>$

We know, by angle sum property, the sum of angles of a quadrilateral is 360°