Sum of Interior Angles in a Polygon

Q.

Find $\angle ABF$ from the given figure.

1. 30º

2. 45º

3. 75º

4. 60º

Q.

In the given figure AB is the side of a regular octagon and BC is the side of a regular hexagon. Find $\angle$ AOC.

1. ${100}^o$

2. ${115}^o$

3. ${95}^o$

4. ${105}^o$

Q.

If the sum of the interior angles of a polygon is ${1440}^{\circ }$, then it has ___ sides.

1. 10

2. 16

3. 20

4. 12

Q.

If one interior angle of an octagon is ${310}^{\circ }$ and each of the other angles are $x^{\circ }$, then x = ___

1. ${180}^{\circ }$

2. ${130}^{\circ }$

3. ${140}^{\circ }$

4. ${110}^{\circ }$

Q.

If two interior angles of a hexagon are 70${}^{\circ }$ and 50${}^{\circ }$ and all the remaining interior angles are equal to $x^{\circ }$. Find the value of $x$.

1. 90${}^{\circ }$

2. 100${}^{\circ }$

3. 150${}^{\circ }$

4. 175${}^{\circ }$

Q.

The regular polygon whose exterior angle is ${40}^{\circ }$ is a:

1. Nonagon

2. Decagon

3. Octagon

4. Heptagon

Q.

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

1. 

2. 

3. 

4. 

Q. How many sides does a polygon have, if the sum of all the interior angles of the polygon is 720?

1. 4
2. 5
3. 7
4. 6

Q.

The sum of all the interior angles of a regular octagon is:

1. 

2. 

3. 

4. 

Q.

If the sum of the interior angles of a is five times the sum of its exterior angles, then the number of sides it has is

1. 14

2. 12

3. 11

4. 10

Q. In a given rectangle ABCD, diagonals AD and BC intersect at O. If $\angle COD={120}^{\circ }$, what is the value of $\angle OBA$?

1. ${60}^{\circ }$
2. ${90}^{\circ }$
3. ${45}^{\circ }$
4. none of these

Q. In the given figure, ABCD is a quadrilateral and $\angle ADC=a^{\circ },\angle BCD=b^{\circ }.$ AO and BO are bisectors of $\angle DAB$ and $\angle ABC$ respectively meeting at O. Find $\angle AOB$ in terms of $a^{\circ }$ and $b^{\circ }$.

1. $a+b$
2. $(a+2b)\times 2$
3. $\frac{(a+2b)}{2}$
4. $\frac{a+b}{2}$

Q.

The sum of interior angles of a polygon with 12 sides is___

1. Closed curve
2. Point
3. Line
4. On the boundary

Q. In the given figure, ABCD is a special quadrilateral in which the sum of its opposite internal angles is ${180}^{\circ }$.
What is the value of $\angle FDC$, given $\angle CBE={130}^{\circ }$?

1. ${30}^{\circ }$
2. ${50}^{\circ }$
3. ${75}^{\circ }$
4. ${130}^{\circ }$

Q.

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

Q. In a polygon, there are $5$ right angles and the remaining angles are equal to ${195}^o$ each. Find the number of sides in the polygon.

1. $5$
2. $11$
3. $8$
4. $7$

Q.

In the given figure, find the value of 'x'.

1. ${30}^{\circ }$
2. ${40}^{\circ }$
3. ${60}^{\circ }$
4. ${50}^{\circ }$

Q. If all the angles of a hexagon are equal. Find the measure of each of its angle.

1. ${100}^{\circ }$
2. ${240}^{\circ }$
3. ${140}^{\circ }$
4. ${120}^{\circ }$