Sum of Angles of a Polygon

Q.

The angles of a quadrilateral are in ratio $4:5:7:8$. Find the measure of each angle.

Q.

If the sum of interior angles of a polygon is 900°, then the it is a ___.

1. 
2. 
3. 
4. 

Q.

If the perimeter of a regular octagon is $72cm$, then its side is

1. $6cm$

2. $8cm$

3. $9cm$

4. $12cm$

Q.

What is the sum of interior angles of a square?

1. 5 lines
2. Curve
3. Closed curve
4. Polygon

Q.

If the angles of a quadrilateral are in the ratio $2:3:4:6$, find the angles.

Q.

Find the perimeter of a regular octagon with side $6.5cm$.

Q. The ratio of inner to outer angle at one corner of a regular polygon is 11 : 7. Find the interior angle.

1. 110

Q. Find the number of sides of a polygon, if the sum of its interior angles is ${1620}^{\circ }$

1. 11
2. 9
3. 10
4. 12

Q.

The angles $P,Q,R$ and $S$ of a quadrilateral are in the ratio $1:3:7:9$. Then $PQRS$ is a

1. parallelogram

2. trapezium with PQ || RS

3. trapezium with QR||PS

4. kite

Q.

In a regular polygon if the ratio of exterior angle to its interior angle is 2 : 7, then the polygon has ___ sides.

1. 8

2. 9

3. 10

4. 6

Q.

If the sum of interior angles of a polygon is 16 right angles, then it has ___ sides.

1. Square

2. Circle

3. Rhombus

4. Trapezium

Q. Match the following polygons with their respective sum of interior angles

1. ${720}^{\circ }$
2. ${180}^{\circ }$
3. ${360}^{\circ }$
4. ${540}^{\circ }$

Q.

Sum of interior angles of a polygon of n sides = _____.

1. (2n - 4) × 90°

2. (2n - 1) × 90°

3. (2n - 2) × 90°

4. (4n - 2) × 90°

Q. The angles of a hexagon are ${(2x+5)}^{\circ },{(3x-5)}^{\circ },{(x+35)}^{\circ },{(2x+20)}^{\circ },{(2x+25)}^{\circ }$ and ${(2x+30)}^{\circ }$. Find the value of $x$.

1. $x=42$
2. $x=75$
3. $x=50$
4. $x=35$

Q.

The sum of the angles of a quadrilateral is

1. 180$°$

2. 270$°$

3. 360$°$

4. 540$°$

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 x = ___.

1. 120°

2. 160°

3. 150°

4. 140°

Q.

In which of the following quadrilaterals is a diagonal not an angle bisector?

1. Rectangle

2. Square

3. Rectangle

4. None of These

Q.

In which of the following quadrilaterals, is a diagonal not an angle bisector?

1. Square

2. Rectangle

3. Rectangle

4. None of These

Q.

If the angles of a quadrilateral are in the ratio 3:4:6:7, then the quadrilateral is a___.

1. Angles A & B

2. Angles B & C

3. Angles A & C

4. Angles C & D

Q.

If the sum of the interior angles of a polygon is two times the sum of its exterior angles, then the polygon has ___ sides.

1. 7

2. 6

3. 5

4. 8

Q.

Which of the following can never be the measure of exterior angle of a regular polygon?

1. $22°$

2. $36°$

3. $45°$

4. $30°$

Q.

The sum of interior angles of a quadrilateral is ___ degrees.

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

Q.

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

1. 12

2. 11

3. 10

4. 9

Q. One exterior angle of regular polygon measures ${10}^o$ What is the measures of each interior angle? How many sides does the polygon have?

Q.

If the interior angle of a regular polygon is equal to its exterior angle, then the polygon has _____ sides.

1. 5

2. 6

3. 7

4. 4

Q.

Three angles of a quadrilateral are equal and the fourth angle measures $120°$. What is the measure of each of the equal angles?

Q.

Find the measure of the angles of a quadrilateral if the angles are in the ratio $2:5:9:2.$

Q. The angles of a pentagon are in the ratio $4:8:6:4:5$. Find each angle of the pentagon.

1. ${40}^{\circ },{160}^{\circ },{120}^{\circ },{80}^{\circ }and{100}^{\circ }$
2. ${60}^{\circ },{160}^{\circ },{120}^{\circ },{80}^{\circ }and{100}^{\circ }$
3. ${80}^{\circ },{160}^{\circ },{120}^{\circ },{80}^{\circ }and{100}^{\circ }$
4. ${30}^{\circ },{160}^{\circ },{120}^{\circ },{80}^{\circ }and{100}^{\circ }$

Q.

If each interior angle of a regular polygon is 120°, then it has ___ sides.

1. 11

2. 12

3. 6

4. 9