Mixed Regular Polygons

Q.

The figure shows 3 regular pentagons put together. The measure of $\angle ABC$ is

1. ${36}^{\circ }$

2. ${63}^{\circ }$

3. ${72}^{\circ }$

4. ${27}^{\circ }$

Q.

In the given figure, regular pentagons are drawn on each side of an equilateral triangle. The measure each angle between the pentagons is

1. ${84}^{\circ }$

2. ${94}^{\circ }$

3. ${54}^{\circ }$

4. ${64}^{\circ }$

Q.

The figure shows a regular pentagon, a regular hexagon and an equilateral triangle put together. The measure of $\angle PQR$ is

1. ${62}^{\circ }$

2. ${72}^{\circ }$

3. ${52}^{\circ }$

4. ${82}^{\circ }$

Q.

The figure shows a regular pentagon, a regular hexagon and a regular octagon put together . The measure of $\angle ABC$ and $\angle ADE$ are

1. ${132}^{\circ },{105}^{\circ }$

2. ${105}^{\circ },{132}^{\circ }$

3. ${100}^{\circ },{137}^{\circ }$

4. ${110}^{\circ },{112}^{\circ }$

Q.

The figure shows a regular pentagon and equilateral triangles are put together. Then which of the following statements are true?

1. $\angle ABC={142}^{\circ }$

2. $\angle ABC={132}^{\circ }$

3. $\angle ABC=\angle CDE=\angle EFG$

4. $\angle BDF={108}^{\circ }$

Q.

The figure shows a regular pentagon and two regular hexagons put together. The measure of $\angle ABC$ is

1. ${14}^{\circ }$

2. ${16}^{\circ }$

3. ${10}^{\circ }$

4. ${12}^{\circ }$

Q.

In the given figure, regular pentagons are drawn on each side of an equilateral triangle. Then find the measure of each angle between the pentagons. $\left[4\right]$

Q.

The measures of angles of the rhombus given in the diagram are

1. ${60}^{\circ },{120}^{\circ },{60}^{\circ }{120}^{\circ }$

2. ${50}^{\circ },{130}^{\circ },{50}^{\circ }{130}^{\circ }$

3. ${30}^{\circ },{150}^{\circ },{30}^{\circ }{150}^{\circ }$

4. ${40}^{\circ },{140}^{\circ },{40}^{\circ }{140}^{\circ }$

Q. The angle of a hexagon are $x+{10}^o,2x+{20}^o,2x-{20}^o,3x-{50}^o,x+{40}^o$ and $x+{20}^o$. Find $x$.

Q.

If all sides of a hexagon are equal then the angles are

1. Never equal

2. None

3. Need not be equal

4. Always equal

Q.

In the given figure, regular pentagons are drawn on each side of an equilateral triangle. The measure each angle between the pentagons is

1. ${84}^{\circ }$

2. ${94}^{\circ }$

3. ${64}^{\circ }$

4. ${54}^{\circ }$

Q.

The measures of angles of the rhombus given in the diagram are

1. ${60}^{\circ },{120}^{\circ },{60}^{\circ }{120}^{\circ }$
   

2. ${50}^{\circ },{130}^{\circ },{50}^{\circ }{130}^{\circ }$
   

3. ${30}^{\circ },{150}^{\circ },{30}^{\circ }{150}^{\circ }$
   

4. ${40}^{\circ },{140}^{\circ },{40}^{\circ }{140}^{\circ }$

Q.

Find $\angle ABF$ from the given figure.

1. ${60}^{\circ }$

2. ${75}^{\circ }$

3. ${30}^{\circ }$

4. ${45}^{\circ }$

Q.

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

1. ${171}^{\circ }$

2. ${117}^{\circ }$

3. ${127}^{\circ }$

4. ${107}^{\circ }$