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

Answer:

2. Trapezium

Step-by-step explanation:

A parallelogram has two sets of similar angles. So all the ratio cannot be different.

A kite also has two sets of similar (opposite) angles.

A trapezium has two parallel sides and therefore, all the angles can differ.

However, the there are two sets of angles, and in each set, the angles are supplementary to each other (by properties of parallel lines).

If we solve using these equation:

∠1 + ∠2 = 180 and ∠1/∠2 = 3/2

and

∠3+∠4 = 180 and ∠3/∠4 = 1/4

We will end up with 108°, 72°, 36° and 144°.

Hence, the answer is a trapezium snce all angles are different.

Answer 2

Step-by-step explanation:

Answer:

2. Trapezium

Step-by-step explanation:

A parallelogram has two sets of similar angles. So all the ratio cannot be different.

A kite also has two sets of similar (opposite) angles.

A trapezium has two parallel sides and therefore, all the angles can differ.

However, the there are two sets of angles, and in each set, the angles are supplementary to each other (by properties of parallel lines).

If we solve using these equation:

∠1 + ∠2 = 180 and ∠1/∠2 = 3/2

and

∠3+∠4 = 180 and ∠3/∠4 = 1/4

We will end up with 108°, 72°, 36° and 144°.

Hence, the answer is a trapezium snce all angles are different.