If angles A, B, C and D of the quadrilateral ABCD, taken in order, are in the ratio 3:7:6:4,
then name the type of quadrilateral ABCD.
Answers
Answer:
x = 18°
The quadrilateral formed is a Trapezium.
Step-by-step explanation:
The angles are in the ration 3:7:6:4
Let us assume the angles to be 3x, 7x, 6x, 4x.
[Check figure]
We know that in a quadrilateral, the sum of all the angles combined is 360°, So the sum of 3x, 4x, 6x, 7x is 360°.
⇒ 3x + 7x + 6x + 4x = 360° [ASP of a Quadrilateral]
⇒ 20x = 360°
⇒ x = 360°/20
⇒ x = 18°
∠A = 3x = 3(18) = 54°
∠B = 7x = 7(18) = 126°
∠C = 6x = 6(18) = 108°
∠D = 4x = 4(18) = 72°
Before we identify the quadrilateral, we'll state the properties of the quadrilaterals, then eliminate options.
- Rectangle - All angles are 90°.
- Square - All angles are 90°
- Parallelogram - Opposite angles are equal.
- Kite - The opposite angles at the ends of one diagonal are equal.
- Trapezium - Two angles on the same side are supplementary.
Now, let's rule out a couple of options.
- It cant be a rectangle, or a square as none of the angles we've found are of 90°.
- It cant be a parallelogram as opposite angles are not equal.
- It cant be a kite as no pair of opposite angles are equal.
- The last option we have is a Trapezium.
Now, We'll prove that the quadrilateral is a Trapezium.
In a trapezium, adjacent angles are supplementary.
∠A + ∠B = 180°
54° + 126° = 180°
180° = 180°
LHS = RHS
Hence the following quadrilateral is a Trapezium.
