Question

1. The angles A, B, C and D of a quadrilateral ABCD are in the ratio 2:4:5:7. Find the
measures of these angles. What type of quadrilateral is it? Give reasons.
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Answer 1

Answer:

Let the angles be 2x, 4x, 5x and 7x

Using ASP of a quadrilateral,

2x+4x+5x+7x = 360

18x  =  360

x = 360/18

x = 20

So, the angles are

2x = 40

4x = 80

5x = 100

7x = 140

If we draw the figure, we notice it is a trapezium.

Numerically, we can see that

B + C

= 80 + 100 = 180

and

A + D

= 40 + 140 = 180

As the co-interior angles are supplementary, AB ║ CD.

As one pair of opposite sides is parallel, it is a trapezium.

Answer 2

Answer:

Let the angles be 2x,4x,5x and 7x.

We know that the sum of all the angles of a quadrilateral is 360°.

=> 2x+4x+5x+7x =360°

=> 18x=360°

=> x=360/18

=>x= 20°

Hence, the angles are : 2×20=40°, 4×20=80°,5×20=100°, 7×20=140°.

As the sum of supplementry angles of quadrilateral is 180°, it is a trapezium.