Question

the angles of a quadrilateral are in the ratio 3:4:5:6.show that the quadrilateral is a trapezium?

Answer 1

hello,
let the quad ABCD with angles in ratio 3:4:5:6
let the angles be 3x,4x,5x,6x
3x+4x+5x+6x=360° (angle sum property of quad.)
18x=360°
x=20
therefore,the angles are
3x=3·20=60°-A
4x=4·20=80°-B
5x=5·20=100°-C
6x=6·20=120°-D
now,A and D are supplementary
and,B and C are supplementary
∴AB║CD
when 2 opposite sides are parallel,the the quad. is trapezium
hope this helps u,if u like it please mark it as brainliest

Answer 2

Let the all angles of quadrilateral be 3x,4x,5x,6x.

we know that,
sum of all angles of quadrilateral = 360
• 3x + 4x + 5x + 6x = 360
• 18x = 360
• x = 360÷18 = 20

Now, all angles of triangle will be 60,80,100,120

clearly here
60+120 = 80+100
180 = 180

Since the sum of interior angles on same side is 180, their exists one pair of parallel side.
Hence the quadrilateral is a trapezium....
.•. hence proved..