Question

In a quadrilateral PQRS the angles are in the ratio of 3: 4: 5: 6 .find the angles of PQRS what is the special name given to PQRS

Answer 1

Ratio of angles = 3:4:5:6
angles are P=3x, Q=4x, R=5x, S=6x
sum = 3x+4x+5x+6x = 360
⇒18x = 360
⇒x = 360/18 = 20

angles are
P= 3x = 20*3 =60
Q= 4x = 20*4 = 80
R= 5x = 20*5 = 100
S= 6x = 620*6 = 120

P+R=180
Q+S=180
Since sum of opposite angles = 180, The special name of this quadrilateral is cyclic quadrilateral.

Answer 2

ratio = 3 : 4 : 5 : 6 
let angles = P =  3x
                 Q =  4x
                 R =  5x
                 S =  6x
sum = 3x + 4x + 5x + 6x = 360
18x = 360
x = 360/18
x = 20
angles = 3x = 3*20 = 60
             4x = 4*20 = 80
             5x = 5*20 = 100
             6x = 6*20 = 120
but , P+ S = 60 + 120 = 180
       Q + R = 80 + 100 = 180
opposite angles are supplementary.
therefore it is a cyclic quadrilateral.