Concave and Convex Polygons

Q.

Sum of all interior angles of a nonagon is

1. 1080^o

2. 1460^o

3. 1260^o

4. 1620^o

Q. If each angle of the polygon is less than ${180}^{\circ }$, then it is known as

1. Irregular polygon
2. Concave polygon
3. Convex polygon
4. Regular polygon

Q.

The given figure is a convex polygon.

.

Q.

A convex polygon has at least one diagonal external to it.

1. False

2. True

Q.

Why is a rectangle a convex quadrilateral?

Q.

Which of the following are concave polygons?

1. i, ii, iii

2. ii, iii, iv

3. ii, iii

4. none of these

Q.

If the sum of the interior angles of a convex polygon is (4 180^o). What kind of polygon is it?

1. Pentagon

2. Hexagon

3. Triangle

4. Quadrilateral

Q.

Sum of all interior angles of a nonagon is

1. 1260^o

2. 1080^o

3. 1620^o

4. 1460^o

Q. The angle sum of a convex polygon of 7 sides is _______.

Q. If the sum of all interior angles of a convex polygon is ${1440}^{\circ }$, then the number of sides of the polygon is?

1. $8$
2. $11$
3. $10$
4. $12$

Q. What is the sum of the measures of the angles of a convex quadrilateral ? Will this property hold if the quadrilateral is not convex

Q. prove that the sum of all interior angles in a convex quadrilateral is (n-2)180 degrees.

Q. The measure of each exterior angle of a regular polygon of 15 sides is:

1. 280 degrees
2. 24 degrees
3. 360 degrees
4. 156 degrees

Q.

If two interior angles of a hexagon are 70${}^{\circ }$ and 50${}^{\circ }$ and all the remaining interior angles are equal to $x^{\circ }$ then this hexagon is a concave polygon.

1. True

2. False

Q. The measure of each exterior angle of a regular polygon of 15 sides is:

1. 360 degrees
2. 280 degrees
3. 24 degrees
4. 156 degrees

Q. Examine the table
What can you say about the angle sum of a convex polygon with number of sides 7

1. ${900}^o$
2. ${980}^o$
3. ${1080}^o$
4. ${720}^o$

Q.

If the sum of the interior angles of a convex polygon is (4 x 180^o). What kind of polygon is it?

1. Hexagon

2. Pentagon

3. Quadrilateral

4. Triangle

Q. Question 5 (a)
(a) Is it possible to have a regular polygon with measure of each exterior angle as ${22}^{\circ }$?

Q. how many diagonals does a concave hexagon have?

Q. The measure of each exterior angle of a regular polygon of 15 sides is:

1. 24 degrees
2. 156 degrees
3. 360 degrees
4. 280 degrees

Q.

A polygon is said to be a concave polygon if

1. atleast one angle is less than 360°

2. atleast one angle is greater than 180°

3. atleast one angle is greater than 90°

4. each angle is greater than 90°

Q. The sum of the angles of a polygon is ${8100}^0$. How many sides does it have? [2 Marks]

Q. If at least one interior angle of a polygon is greater than 180 degrees, then the polygon is called:

1. Convex Polygon
2. Concave Polygon
3. Regular Polygon
4. Irregular Polygon

Q. (A) The diagonals are perpendicular to each other.
(B) The diagonals bisect each other.
(C) Only one pair of opposite angles is equal.
(D) All the four sides are equal.
Which one of these is false for a kite?

1. The diagonals are perpendicular to each other
2. The diagonals bisect each other.
3. Only one pair of opposite angles is equal.
4. All the four sides are equal

Q. The diagonals of quadrilateral intersect at right angles and it has exactly one axis of symmetry. Which type of quadrilateral is it?

1. rhombus
2. square
3. kite
4. rectangle

Q. The measure of each interior angle of a regular convex polygon is ${156}^{\circ }$. Find the number of sides this polygon has.

1. 12
2. 10
3. 8
4. 15

Q.

A polygon having eight sides, is called:

1. Octagon

2. Pentagon

3. Hexagon

4. Heptagon

Q. Can convex polygons also be called irregular polygons? Justify.

Q.

is a kite a concave or convex polygon?

Q. The measure of each exterior angle of a regular polygon of 15 sides is:

1. 280 degrees
2. 24 degrees
3. 360 degrees
4. 156 degrees