Quadrilateral Angle Ratio and Classification: Parallelogram or Rhombus?

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In summary, the angles of a quadrilateral with a ratio of 2:7:2:7 are in a parallelogram, but not necessarily a rhombus.
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mpx86
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Homework Statement


If angles of a quadrilateral are in the ratio 2:7:2:7, then the quadrilateral is?
a) Square
b) Rectangle
c) Rhombus
d) Parallelogram

Homework Equations


2x+7x+2x+7x= 360
x=20[/B]

The Attempt at a Solution


Since two pairs of opposite angles of a quadrilateral are equal, hence it must be a parallelogram...
The book says rhombus as an answer... The book is wrong... Right?[/B]
 
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  • #2
mpx86 said:

Homework Statement


If angles of a quadrilateral are in the ratio 2:7:2:7, then the quadrilateral is?
a) Square
b) Rectangle
c) Rhombus
d) Parallelogram

Homework Equations


2x+7x+2x+7x= 360
x=20[/B]

The Attempt at a Solution


Since two pairs of opposite angles of a quadrilateral are equal, hence it must be a parallelogram...
The book says rhombus as an answer... The book is wrong... Right?[/B]

Right. It has to be a parallelogram. It doesn't have to be a rhombus (though it might be).
 

1. What is a quadrilateral?

A quadrilateral is a two-dimensional geometric shape with four sides, four angles, and four vertices.

2. What are the types of quadrilaterals?

The types of quadrilaterals include rectangle, square, parallelogram, rhombus, trapezoid, and kite.

3. How are quadrilaterals classified?

Quadrilaterals are classified based on their properties, such as the length of their sides, the measure of their angles, and the types of their angles.

4. How do you determine the type of a quadrilateral?

To determine the type of a quadrilateral, you can use its properties, such as the length of its sides, the measure of its angles, and the types of its angles. You can also use mathematical formulas and theorems specific to each type of quadrilateral.

5. Can a quadrilateral have more than one type?

Yes, a quadrilateral can have more than one type. For example, a square is also a rectangle, a rhombus, and a parallelogram. It depends on the properties and characteristics of the quadrilateral.

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