Question

if the angle of a quadriateral are in the ratio 3: 2: 1: 4 then what is the type of quardriateral​

Answer 1

Answer :

• Trapezium is the type of Quadrilateral

Given :

• The angle of a Quadrilateral are in the ratio 3:2:1:4

To find :

• Type of Quadrilateral

Solution :

• Let the ratio be 3x , 2x , x and 4x

As we know that,

• Sum of four angles in a Quadrilateral is equal to 360⁰

》3x + 2x + x + 4x = 360⁰

》10x = 360⁰

》x = 360⁰/10

》x = 36⁰

Then,

• 3x = 3(36) = 108⁰
• 2x = 2(36) = 72⁰
• x = 36⁰
• 4x = 4(36) = 144⁰

So, This angles are different, Then it's a trapezium.

Trapezium is the type of Quadrilateral

Answer 2

Answer:

Given:

• Ratio of angles of quadrilateral = 3: 2: 1: 4

Find:

• Type of quadrilateral?

Solution:

• Let the angles are 3x , 2x, 1x, 4x
• Sum of all angles in quadrilateral = 360°

$: { \implies { \sf{3x + 2x + 1x + 4x = 360}}} \\ \\ : { \implies { \sf{5x + 5x = 360}}} \\ \\ : { \implies { \sf{10x = 360}}} \\ \\ : { \implies { \sf{ x = 36}}}$

Let's find the angles:-

➙ 3x = 3 × 36 = 108°

➙ 2x = 2 × 36 = 72°

➙ 1x = 1 × 36 = 36°

➙ 4x = 4 × 36 = 144°

The following quadrilateral is Trapezium, because all the angles are different.

Therefore,

• The type of quadrilateral is Trapezium