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Q.

Choose the option which indicates the sum of all the interior angles of a concave quadrilateral.


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a

More than 360°

b

Less than 360°

c

Equal to 360°

d

Twice of 360° 

answer is C.

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Detailed Solution

We need to find the sum of all the interior angles of a concave quadrilateral.
A polygon is said to be a quadrilateral, when it has four sides which form a closed two-dimensional shape. Now, the necessary condition for a quadrilateral to be concave is that one of its interior must be greater than 180 ° .
Next, for any polygon, the sum of all its interior angles is mathematically given as, n−2 × 180 ° , where n is the number of sides.
Now, as a quadrilateral has 4 sides, so we will substitute 4 for n in the formula above, to get the sum of all the interior angles as follows,
4−2 × 180 ° 2× 180 ° 360 °
So, the sum of all the interior angles of a concave quadrilateral is found to be 360 ° .
Hence, the correct option is (3).
 
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