Question

A concave polygon has _____ interior angles more than $${180}^{\circ }$$.
(a) no
(b) 3 angles
(c) one or more
(d) less than 5

Answer 1

Hint: A concave polygon is a polygon with sides more than 4. Draw a concave polygon, if measuring the angle we will get angles that are greater than $${180}^{\circ }$$. Take the example of a star to prove the same.

Complete step-by-step answer:
A polygon which has at least one angle that measures more than $${180}^{\circ }$$ is called a concave polygon. The vertices of this polygon are inwards as well as outwards.
The figure shows a concave polygon.
 

A concave polygon has one or more interior angles that are greater than $${180}^{\circ }$$. A concave polygon can have any number of sides but it should be greater than 4.
From the figure you can say that,
$$\mathrm{\angle }ABC={250}^{\circ },\mathrm{\angle }HGF={300}^{\circ }$$
Both these angles are greater than $${180}^{\circ }$$ and they are projected as interior angles of the concave polygon.
All the concave polygons are irregular since the interior angle of the polygons are of different measures. You can also consider a star as a concave polygon as it has one or more interior angles greater than $${180}^{\circ }$$ and has more than 4 sides.
$$\therefore$$ A concave polygon has one or more interior angles more than $${180}^{\circ }$$.
$$\therefore$$ Option (c) is the correct answer.

Note: In a concave polygon one or more interior angles should be greater than $${180}^{\circ }$$. But in a convex polygon, all its interior angles should be less than $${180}^{\circ }$$. The vertices of the polygon will point outwards, away from the interior of the shape.