2 Marks Questions

Question 12 Marks

What is the sum of all interior angles of a regular: Hexagon.

Answer

Sum of the interior angles of an n-sided polygon $= (n - 2) \times 180^\circ ,$ For a hexagon: $\text{n}=6$
$\therefore(\text{n}-2)\times180^\circ=(6-2)\times180^\circ=4\times180^\circ=720^\circ$

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Question 22 Marks

Find the measure of each exterior angle of a regular: Decagon.

Answer

Exterior angle of an n-sided polygon $=\Big(\frac{360}{\text{n}}\Big)^\circ$
For a decagon: $\text{n}=10$
$\therefore\Big(\frac{360}{\text{n}}\Big)=\Big(\frac{360}{\text{10}}\Big)=36^\circ$

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Question 32 Marks

Find the measure of each exterior angle of a regular: Pentagon.

Answer

Exterior angle of an n-sided polygon $=\Big(\frac{360}{\text{n}}\Big)^\circ$ For a pentagon: $\text{n}=5$ $\therefore\Big(\frac{360}{\text{n}}\Big)=\Big(\frac{360}{\text{5}}\Big)=72^\circ$

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Question 42 Marks

What is the sum of all interior angles of a regular:
Pentagon.

Answer

Sum of the interior angles of an n-sided polygon $= (n - 2) \times 180^\circ ,$
For a pentagon:
$\text{n}=5$
$\therefore(\text{n}-2)\times180^\circ=(5-2)\times180^\circ=3\times180^\circ=540^\circ$

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Question 52 Marks

Find the number of sides of a regular polygon whose each exterior angle measures: $30^\circ $

Answer

Sum of all the exterior angles of a regular polygon is $360^\circ .$
Each exterior angle $= 30^\circ ,$
Number of sides of the regular polygon $=\frac{360}{30}=12$

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Question 62 Marks

Find the measure of each interior angle of a regular polygon having:
$10$ sides.

Answer

For a regular polygon with n sides:
each interior angle $= 180 -$ {Each exterior angle} $=180-\Big(\frac{360}{\text{n}}\Big) $
For a polygon with $10$ sides:
Each exterior angle $=\frac{360}{10}=36^\circ$
$\Rightarrow $ Each interior angle $= 180 - 36 = 144^\circ $

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Question 72 Marks

What is the number of diagonals in a:
Heptagon.

Answer

Number of diagonal in an n-sided polygon $=\frac{\text{n}(\text{n}-3)}{2}$
For a heptagon:
$\text{n}=7\Rightarrow\frac{\text{n}(\text{n}-3)}{2}=\frac{7(7-3)}{2}=\frac{28}{2}=14$

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Question 82 Marks

What is the sum of all interior angles of a regular: Nonagon.

Answer

Sum of the interior angles of an n-sided polygon $= (n - 2) \times 180^\circ $
, For a nonagon: $\text{n}=9$
$\therefore(\text{n}-2)\times180^\circ=(9-2)\times180^\circ=7\times180^\circ=1260^\circ$

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Question 92 Marks

Find the number of sides of a regular polygon whose each exterior angle measures: $36^\circ $

Answer

Sum of all the exterior angles of a regular polygon is $360^\circ .$
Each exterior angle $= 36^\circ ,$
Number of sides of the regular polygon $=\frac{360}{36}=10$

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Question 102 Marks

Find the measure of each exterior angle of a regular: Heptagon.

Answer

Exterior angle of an n-sided polygon $=\Big(\frac{360}{\text{n}}\Big)^\circ$ For a heptagon: $\text{n}=7$ $\therefore\Big(\frac{360}{\text{n}}\Big)=\Big(\frac{360}{\text{7}}\Big)=51.43^\circ$

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Question 112 Marks

Find the measure of each exterior angle of a regular: Hexagon.

Answer

Exterior angle of an n-sided polygon $=\Big(\frac{360}{\text{n}}\Big)^\circ$ For a hexagon: $\text{n}=6$ $\therefore\Big(\frac{360}{\text{n}}\Big)=\Big(\frac{360}{\text{5}}\Big)=60^\circ$

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Question 122 Marks

Find the measure of each interior angle of a regular polygon having: $15$ sides.

Answer

For a regular polygon with n sides: each interior angle $= 180 -$ {Each exterior angle} $=180-\Big(\frac{360}{\text{n}}\Big) $ For a polygon with $15$ sides: Each exterior angle $=\frac{360}{15}=24^\circ$
$\Rightarrow $ Each interior angle $= 180 - 24 = 156^\circ $

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Question 132 Marks

Find the number of sides of a regular polygon whose each exterior angle measures: $40^\circ $

Answer

Sum of all the exterior angles of a regular polygon is $360^\circ .$
Each exterior angle $= 40^\circ ,$
Number of sides of the regular polygon $=\frac{360}{40}=9$

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Question 142 Marks

Find the measure of each exterior angle of a regular: Polygon of $15$ sides.

Answer

Exterior angle of an n-sided polygon $=\Big(\frac{360}{\text{n}}\Big)^\circ$ For a polygon of $15$ sides: $\text{n}=15$ $\therefore\Big(\frac{360}{\text{n}}\Big)=\Big(\frac{360}{\text{15}}\Big)=24^\circ$

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Question 152 Marks

Is it possible to have a regular polygon each of whose exterior angles is $50^\circ ?$

Answer

Each exterior angle of an n-sided polygon $=\Big(\frac{360}{\text{n}}\Big)^\circ$ If the exterior angle is $50^\circ $,
then: $\frac{360}{\text{n}}=50$
$\Rightarrow\text{n}=7.2$

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Question 162 Marks

Find the number of sides of a regular polygon whose each exterior angle measures: $72^\circ $

Answer

Sum of all the exterior angles of a regular polygon is $360^\circ .$
Each exterior angle $= 72^\circ ,$
Number of sides of the regular polygon $=\frac{360}{72}=5$

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Question 172 Marks

What is the number of diagonals in a: Polygon of $12$ sides?

Answer

Number of diagonal in an n-sided polygon $=\frac{\text{n}(\text{n}-3)}{2}$
For a $12$-sides polygon: $\text{n}=12\Rightarrow\frac{\text{n}(\text{n}-3)}{2}=\frac{12(12-3)}{2}=\frac{108}{2}=54$

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Question 182 Marks

What is the number of diagonals in a: Octagon.

Answer

Number of diagonal in an n-sided polygon $=\frac{\text{n}(\text{n}-3)}{2}$
For a octagon: $\text{n}=8\Rightarrow\frac{\text{n}(\text{n}-3)}{2}=\frac{8(8-3)}{2}=\frac{40}{2}=20$

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Question 192 Marks

What is the sum of all interior angles of a regular: Polygon of $12$ sides?

Answer

Sum of the interior angles of an n-sided polygon $= (n - 2) \times 180^\circ ,$
For a polygon of $12$ sides: $\text{n}=12$
$\therefore(\text{n}-2)\times180^\circ=(12-2)\times180^\circ=10\times180^\circ=1800^\circ$

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