Question

If the angles of a quadrilateral,taken in order are in the ratio 1:2:3:4, prove that it is a trapezium

Answer 1

By this,we get the measuresbof the angles as 36°,72°,108° and 144° respectively.We also get to see that 72° and 108° ,which are adjacent angles,when added up give 180°.As we know that one pair of adjacent angles of a trapezium is supplementary,

Thus,these angles are of a trapezium.

Hence proved.

I hope that helps and is clear enough for you to understand.

Btw please mark this answer as 'Branliest'.

Answer 2

Let's assume the angles as

x°, 2x°, 3x° & 4x°

We know,

Sum of all ∠s of Trapezium = 360°

According to Question,

x + 2x + 3x + 4x = 360

⇒ 10x = 360

⇒ x = 360 / 10

⇒ x = 36

Required ∠s »

x° = 36°

2x° = 2(36)° = 72°

3x° = 3(36)° = 108°

4x° = 4(36)° = 144°

∵ 36° + 72° + 108° + 144° = 360

Since, the sum of ∠s of Trapezium is 360°

Hence, it is a Trapezium.

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