The angles of quadrilateral are in the ratio 3 : 5 : 9 : 13. Find all the angles of the quadrilateral.
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Step-by-step explanation:
Let angle in the ratio 3:5:9:13 be a,b,c,d
Let a=3x,b=5x,,c=9x,d=13x
where x is any number
We know that
Sum of angle of quadrilateral is 360
o
a+b+c+d=360
o
[Angle sum property of quadrilateral]
3x+5x+9x+13x=360
o
30x=360
o
x=
30
360
o
x=12
o
Hence the angles are
a=3x=3×12
o
=36
o
b=5x=5×12
o
=60
o
c=9x=9×12
o
=108
o
d=13x=13×12
o
=156
o
Verified answer
Step-by-step explanation:
Area (ΔHEF) = 1/2Area (ABFH) … (1)
Similarly, it can be proved that
)
On adding equations (1) and (2), we get
area of ΔEFH + area of ΔGHF = ½ ar
⇒ area of EFGH = area of ABFH