Question

ratio between the four angles of a quadrilateral is 2:4:5:7. can you say that the quadrilateral is a trapezium.​

Answer 1

Given :

ratio between the four angles of a quadrilateral is 2:4:5:7.

To prove :

the quadrilateral is a trapezium.

Solution :

the angles of a quadrilateral are in the ratio 2:4:5:7

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

⇛ 2x + 4x + 5x + 7x = 360°

⇛ 18x = 360°

⇛ x = 360/18

⇛ x = 20

Therefore the angles are

⇛ 2 x 20 = 40°

⇛ 4 x 20 = 80°

⇛ 5 x 20 = 100°

⇛ 7 x 20 = 140°

⁛ Since all the angles are of different degrees thus forms a trapezium

Answer 2

Given:

• Ratio between the four angles of a quadrilateral = 2:4:5:7

Need to Find:

• Is it a trapizium?

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Answer:

Let the angles be

• 2x
• 4x
• 5x
• 7x

we know sum of all angles of a quadrilateral =360°

==> 2x+ 4x+ 5x+ 7x = 360°

==> 18x= 360°

==> x = 20

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The angles are:

● 2x

=2× 20

= 40°

● 4x

= 4× 20

= 80°

● 5x

= 5 × 20

=100°

●7x

= 7× 20

= 140°

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As we know, in a trapizium none of the angles are equal to each other,

We can say the given ratio of angles are of a trapizium.