Question

*If the angles of a quadrilateral are in the ratio 3: 2: 1: 4 then what is the type of quadrilateral*

1️⃣ Parallelogram
2️⃣ Trapezium
3️⃣ Kite
4️⃣ none of these​

Answer 1

We can see measure of all 4 angles are different so, the given quadrilateral is trapezium.

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Answer 2

Given :- If the angles of a quadrilateral are in the ratio 3: 2: 1: 4 then what is the type of quadrilateral*

1️⃣ Parallelogram

2️⃣ Trapezium

3️⃣ Kite

4️⃣ none of these

Answer :-

Let the angles be 3x , 2x , x and 4x .

so,

→ Sum of all angles of a quadrilateral = 360°

→ 3x + 2x + x + 4x = 360°

→ 10x = 360°

→ x = 36° .

then , angles are ,

• 3x = 36*3 = 108°
• 2x = 36*2 = 72°
• x = 36°
• 4x = 36*4 = 144° .

now we know,

• The sum of the two adjacent angles of a trapezium is equal to 180°.

, as we can see that,

• x + 4x = 36° + 144° = 180°
• 3x + 2x = 108° + 72° = 180° .

therefore, we can conclude that, the given quadrilateral is a Trapezium (Option 2) (Ans.)

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