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How Many Angles Does a Quadrilateral Have?

TopQuadrilateral is a figure which contains four edges or boundaries and four corners. These corners are called as vertices. So, question arises here is: how many angles does a quadrilateral have? The answer to it is 4. There are four interior angles in a quadrilateral. Measures of angles formed depend on type of quadrilateral, whether it is a Square or a Rectangle or a Parallelogram or trapezium or Rhombus or a kite. Properties of interior angles have two conclusions, which are:

1. Sum of opposite angles in a quadrilateral is 180 degrees or we can say that opposite pairs of angles in any quadrilateral are supplementary.

2. Sum of all angles in a quadrilateral is equals to 360 degrees. So, if we know three angles, then fourth one can be found by using this simple corollary.

Let us take some examples to know more about angles of a quadrilateral
Example 1: In given quadrilateral find the missing angle?
 
 
 
Solution: In the given quadrilateral we have three angles with measures 80 degrees, 94 degrees and 68 degrees. Let the measure of fourth angle be 'x' degrees. According to angle sum property of quadrilaterals we can write:
80 + 94 + 68 + x = 3600,
Or x = 360 – (80 + 94 + 68) = 360 – 242 = 1180.

So, we see that a quadrilateral can contain a Combination of both acute and obtuse angles as its interior angles.
Depending on the shape of quadrilateral we decide the measure of angles like in a square we cannot have an angle more than or less than 900. Same is true for rectangle and rhombus also. In case of quadrilaterals like parallelogram and trapezium we can have both acute and obtuse angles.