Interior Angle in a Regular Polygon

Q.

If each interior angle of a regular polygon is ${150}^{\circ }$, how many sides does this polygon have?

1. $18$

2. $14$

3. $16$

4. $12$

Q.

The ratio between exterior angle and interior angle of a regular polygon is 1 : 5. Find the number of sides of the polygon.

1. $16$

2. $12$

3. $13$

4. $14$

Q. If each interior angle of a regular polygon is ${150}^{\circ }$, how many sides does this polygon have? [3 MARKS]

Q.

Why $120°$ degree is the highest exterior angle for a regular polygon?

Q.

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

1. 

2. 

3. 

4. 

Q. Find the measure of interior angle of a regular octagon.

Q.

What is the formula for finding the exterior and interior angles of a regular polygon?

Q. Question 1
Find x in the following figures:

Q. Question 167
Find the measure of each angle of a regular octagon.

Q.

If each interior angle of a regular polygon is $135°$ how many sides does it have ?

1. $6$

2. $7$

3. $8$

4. $9$

Q.

Each interior angle of a regular polygon is $150°$ . How many sides does it have ?

1. $10$

2. $11$

3. $12$

4. $8$

Q. Is it possible to have a polygon whose sum of interior angles is ${320}^{\circ }$?

1. Yes
2. No
3. Ambiguous
4. Data not sufficient

Q. How many sides does a regular polygon have, if measure of each of its interior angle is ${160}^o$?

1. $18$
2. $16$
3. $15$
4. $20$

Q. How many sides does a regular polygon have, whose interior angle is eight times its exterior angle?

1. $16$
2. $18$
3. $20$
4. $24$

Q. Difference between the interior and exterior angles of regular polygon is ${60}^{\circ }$. The number of sides in the polygon is

1. $5$
2. $8$
3. $6$
4. $9$

Q. Find the measure of interior angle of a regular octagon.

Q. In the given figure, PQRS is a rectangle if $\angle RPQ={30}^{\circ }$. Then, the value of (x + y) is:

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

2. ${120}^{\circ }$

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

4. ${180}^{\circ }$

Q. Find the number of sides of regular polygon whose measure of each of its interior angle is $\frac{{360}^o}{7}$.

1. $9$
2. $7$
3. $8$
4. $6$

Q. Is it possible to have a regular polygon whose each interior angle is ${150}^{\circ }$

1. No
2. Yes
3. Cannot be determined
4. None of these

Q. Is it possible to have a regular polygon whose each interior angle is ${175}^{\circ }$

1. True
2. False

Q. If $S$ denotes the sum of all the interior angles of a polygon of $n$ sides, then the number of right angles in $S$ is:

1. $(n-1)$
2. $2(n-1)$
3. $2(n-2)$
4. $2n$

Q. Is it possible to have a polygon whose sum of interior angles is $11$ right angles?

1. Yes
2. No
3. Ambiguous
4. Data insufficient

Q. Find the measure of each interior angle of a consecutive regular polygon of $5$ sides.

1. ${130}^{\circ }$
2. ${179}^{\circ }$
3. ${156}^{\circ }$
4. ${108}^{\circ }$

Q. Find the number of sides in a regular polygon if each exterior angle is ${\left[22\frac{1}{2}\right]}^{\circ }$.

1. $16$
2. $8$
3. $10$
4. $15$

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

Q.

Find the measure of interior angle of a regular octagon.

1. ${135}^{\circ }$

2. ${105}^{\circ }$

3. ${145}^{\circ }$

4. ${120}^{\circ }$

Q.

In a regular polygon of 'n' sides, the interior angle is equal to the exterior angle. Find the value of n.

1. 3

2. 4

3. 6

4. 5

Q. Each interior angle of a $n$-sided regular polygon is ${162}^{\circ }$. Find the interior angle of another polygon with $2n$ sides.

1. ${160}^{\circ }$
2. ${171}^{\circ }$
3. one of the above
4. ${155}^{\circ }$

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 [3 Marks]

Q. There is a regular polygon whose each interior angle is ${175}^{\circ }$

1. True
2. False