The angle of a quadrilateral are in a ratio 3:4:5:6.Show that the quadrilateral is a trapezium
Answers
Hey friend,
∵ The angle of a quadrilateral are in a ratio 3:4:5:6
∴ Let the angles be 3x,4x,5x and 6x respectively.
∵ The sum of all the angles of a quadrilateral = 360°
∴ 3x+4x+5x+6x = 360°
or, 18x = 360°
∴ x = 360°/18 = 20°
∴ angles are = (3×20)°,(4×20)°,(5×20°) & (6×20°)
= 60°, 80°, 100° & 120°
∵ the angles are in order
∴ (60° & 120°) and (100° & 80°) will be the two pairs of adjacent angles
and the sum of both the pairs are 180°
∴ the opposite sides are parallel
another possible pairs of adjacent angles can be (60° & 80°) and (100° & 120°)
∵ the sum of the pairs ≠ 180°
∴ these opposite sides will not be parallel
∴ the quadrilateral will have two opposite parallel sides and two opposite non-parallel sides
∴ the only possible quadrilateral satisfying the above conditions is trapezium.
HOPE U FIND IT HELPFUL ............................. :)
The angles of the quadrilateral are in the ratio
3 : 4 : 5 : 6
3x+4x+5x+6x = 360
18x = 360
x = 20
The value of angle a is
3x = 3×20 = 60°
4x = 4×20 = 80°
5x = 5×20 = 100°
6x = 6×20 = 120°
