Sum of Angles of a Polygon

Q.

The sum of interior angles of a hexagon is

1. ${540}^0$

2. ${720}^0$

3. ${900}^0$

4. ${360}^0$

Q.

Each interior angle of a polygon is ${135}^{\circ }$. How many sides does it have?

$\left(a\right)8$

$\left(b\right)7$

$\left(c\right)6$

$\left(d\right)10$

Q.

Each interior angle of a polygon is ${108}^{\circ }$. How many sides does it have ?

Q.

Find the angle measure x in the given figure.

Q. What is a sum of the measures of the exterior angle of polygon.

Q. The sum of the interior angles of pentagon is

1. ${540}^{\circ }$
2. ${360}^{\circ }$
3. ${580}^{\circ }$
4. ${720}^{\circ }$

Q.

Each interior angle of a regular polygon is ${144}^{\circ }$. Then the measure of each interior angle of a regular polygon which has double the number of sides as the first polygon is

1. ${150}^{\circ }$

2. ${152}^{\circ }$

3. ${162}^{\circ }$

4. ${160}^{\circ }$

Q.

The angles of a pentagon are $x^{\circ },(x-10{)}^{\circ },(x+20{)}^{\circ },(2x-44{)}^{\circ }$ and $(2x-70{)}^{\circ }$, then x=___

1. 

2. 

3. 

4. 

Q.

Sum of interior angles of a polygon doesn't depend on the number of sides.

1. True

2. False

Q. Question 4
How many sides does a regular polygon have if each of its interior angles is ${165}^{\circ }$?

Q.

The figure shows a regular heptagon and a regular hexagon are put together. Then the measures of $\angle ABC$ is

1. ${114}^{\circ }$

2. ${122}^{\circ }$

3. ${121}^{\circ }$

4. ${112}^{\circ }$

Q.

If the interior angles of a pentagon are (3x + 4)°, (x + 20)°, (3x - 5)°, (2x + 10)° and (4x - 9)°, then x is equal to

1. 60°

2. 50°

3. 40°

4. 20°

Q.

If each interior angle of a regular polygon is 150°, then it has _____ sides.

1. 12

2. 11

3. 10

4. 9

Q. Find the angle measure x in the following figure:

Q.

In the given figure, ABCD is a square and DEC is equilateral.

The value of x is

1. 45°

2. 30°

3. 20°

4. 15°

Q.

What is the perimeter of a regular heptagon if the length of one of its sides is $5cm$?

1. $42$

2. $35$

3. $28$

4. $30$

Q. If the interior angles of a pentagon are (3x + 4)°, (x + 20)°, (3x - 5)°, (2x + 10)° and (4x - 9)°, then x is equal to

Q. In a convex hexagon, prove that sum of all interior angles is equal to twice the sum of its exterior angles formed by producing the sides in the same order.

Q. Find the angle measure x in the following figure:

Q.

What is the sum of the interior angles of a heptagon?

A. 800$°$

B. 1200$°$

C. 900$°$

D. 1100$°$

Q. In the given diagram, find the value of x in degrees.

Q.

If each interior angle of a regular polygon is 150°, then the polygon has ___ sides.

Q.

In the figure, a regular octagon and a regular pentagon are put together. The measure of $\angle ABC$ is [4 Marks]

Q. The sum of all internal angles of a pentagon is.

1. ${540}^{\circ }$
2. ${340}^{\circ }$
3. ${220}^{\circ }$
4. ${430}^{\circ }$

Q.

Two alternate sides of a regular polygon, when produced, meet at right angles. Find the number of sides of the polygon.

1. 8

2. 10

3. 20

4. 6

Q. In the given diagram, the value of x is ___ degrees.

Q. An exterior angle of a regular polygon having n-sides is more than that of the polygon having $n^2$ sides by ${50}^{\circ }$, then the number of the sides of each polygon are 6 and 38.

1. True
2. False

Q. if one of the interior angle of a regular polygon is found to be $\frac{9}{8}$ times of one of the interior angle of a regular hexagon then the number of sides of the polygon is

1. $8$
2. $14$
3. $12$
4. $10$

Q. The number of sides of two regular polygons $A$ and $B$ are in the ratio $1:3$. If each interior angle of polygon B is ${168}^{\circ }$; find each interior angle of polygon $A$.

1. ${144}^{\circ }$
2. ${134}^{\circ }$
3. ${124}^{\circ }$
4. none of the above

Q. AB, BC and CD are three consecutive sides of a regular polygon. If angle BAC = ${20}^{\circ }$, find the number of sides in the polygon.