MCQ

MCQ 11 Mark

Tick the correct answer in the following? The measure of each exterior angle of a regular polygon is $40^\circ .$ How many sides does it have?

A
$8$
✓
$9$
C
$6$
D
$10$

Answer

Correct option: B.

$9$

Each exterior angle of a regular $n-$sided polygon $=\frac{160}{\text{n}}=40$
$\Rightarrow\text{n}=\frac{360}{\text{40}}=9$

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MCQ 21 Mark

Tick the correct answer in the following? How many diagonals are there in a polygon having $12$ sides?

A
$12$
B
$24$
C
$36$
✓
$54$

Answer

Correct option: D.

$54$

For an $n-$sided polygon:
Number of diagonals $=\frac{\text{n}(\text{n}-3)}{2}$
$\therefore\text{n}=12$
$\Rightarrow\frac{12(12-3)}{2}=54$

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MCQ 31 Mark

Tick the correct answer in the following? In a regular polygon, each interior angle is thrice the exterior angle. The number os sides of the polygon is:

A
$6$
✓
$8$
C
$10$
D
$12$

Answer

Correct option: B.

$8$

For a regular polygon with $n$ sides:
Each exterior angle $=\frac{ 360}{ \text{n}}$
Each interior angle $=180-\frac{360}{\text{n}}$
$\therefore180-\frac{360}{\text{n}}=3\Big(\frac{360}{\text{n}}\Big)$
$\Rightarrow180=4\Big(\frac{360}{\text{n}}\Big)$
$\Rightarrow\text{n}=\frac{4\times360}{180}=8$

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MCQ 41 Mark

Tick the correct answer in the following? How many diagonals are there in a pentagon?

✓
$5$
B
$7$
C
$6$
D
$10$

Answer

Correct option: A.

$5$

For a pentagon: $n = 5$
Number of diagonals $=\frac{\text{n}(\text{n}-3)}{2}=\frac{5(5-3)}{2}=5$

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MCQ 51 Mark

Tick the correct answer in the following? Each interior angle of a polygon is $135^\circ .$ How many sides does it have?

✓
$8$
B
$7$
C
$6$
D
$10$

Answer

Correct option: A.

$8$

Each interior angle for a regular polygon withn$-$sided $=180-\Big(\frac{360}{\text{n}}\Big)$
$180-\Big(\frac{360}{\text{n}}\Big)=135$
$\Rightarrow\Big(\frac{360}{\text{n}}\Big )=45$
$\Rightarrow\text{n}=8$

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MCQ 61 Mark

Tick the correct answer in the following? Each interior angle of a regular decagon is:

A
$60^\circ$
B
$120^\circ$
✓
$144^\circ$
D
$180^\circ$

Answer

Correct option: C.

$144^\circ$

Each interior angle of a regular decagon $=180-\frac{360}{10}=180-36=144^\circ$

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MCQ 71 Mark

Tick the correct answer in the following? A polygon has $27$ diagonals. How many sides does it have?

A
$7$
B
$8$
✓
$9$
D
$12$

Answer

Correct option: C.

$9$

$\frac{\text{n}(\text{n}-3)}{2}=27$
$\Rightarrow(\text{n}-3)=54$
$\Rightarrow\text{n}^2-3\text{n}-54=0$
$\Rightarrow\text{n}^2-9\text{n}+6\text{n}-54=0$
$\Rightarrow\text{n}(\text{n}-9)+6(\text{n}-9)=0$
$\Rightarrow\text{n}=-6\ \text{or}\ \text{n}=9$
Number of sides cannot be negative.
$\therefore\text{n}=9$

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MCQ 81 Mark

Tick the correct answer in the following? How many diagonals are there in a hexagon?

A
$6$
B
$8$
✓
$9$
D
$10$

Answer

Correct option: C.

$9$

Number of diagonals in an $n-$sided polygon $=\frac{\text{n}(\text{n}-3)}{2}$
$\text{n}=6$
$\therefore\frac{\text{n}(\text{n}-3)}{2}=\frac{6(6-3}{2}$
$=\frac{18}{9}=9$

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MCQ 91 Mark

Tick the correct answer in the following? Each interior angle of a polygon is $108^\circ .$ How many sides does it have?

A
$8$
B
$6$
✓
$5$
D
$7$

Answer

Correct option: C.

$5$

Each interior angle for a regular $n-$sided polygon $=180-\Big(\frac{360}{\text{n}}\Big)$
$180-\Big(\frac{360}{\text{n}}\Big)=108$
$\Rightarrow\Big(\frac{360}{\text{n}}\Big )=72$
$\Rightarrow\text{n}=\frac{360}{\text{n}}=5$

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MCQ 101 Mark

Tick the correct answer in the following? Sum of all the interior angles of a hexagon is:

A
$6\ \text{right}\ \angle\text{s}$
✓
$8\ \text{right}\ \angle\text{s}$
C
$9\ \text{right}\ \angle\text{s}$
D
$12\ \text{right}\ \angle\text{s}$

Answer

Correct option: B.

$8\ \text{right}\ \angle\text{s}$

Sum of all the interior angles of a hexagon is $(2n - 4)$ right angles.
For a hexagon:
$\text{n}=6$
$\Rightarrow(2\text{n}-4)\ \text{Right}\ \angle\text{s}=(12- 4)\ \text{right}\ \angle\text{s}=8\ \text{right}\ \angle\text{s}$

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MCQ 111 Mark

Tick the correct answer in the following? How many diagonals are there in an actagon?

✓
$8$
B
$16$
C
$18$
D
$20$

Answer

Correct option: A.

$8$

For a regular $n-$sided polygon:
Number of diagonals $=\frac{\text{n}(\text{n}-3)}{2}$
For an actagon:
$\text{n}=8$
$\frac{8(8-3)}{2}=\frac{40}{2}=20$

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MCQ 121 Mark

Tick the correct answer in the following? The interior angle of a regular polygon exceeds its exterior angle by $108^\circ .$ How many sides does the polygon have?

A
$16$
B
$14$
C
$12$
✓
$10$

Answer

Correct option: D.

$10$

Each exterior angle of a regular polygon $=\frac{360}{\text{n}}$
Each interior angle of a regular polygon $=180-\frac{360}{\text{n}}$
$180-\frac{360}{\text{n}}-108=\frac{360}{\text{n}}$
$\frac{720}{\text{n}}=180-108=72$
$\text{n}=\frac{720}{72}=10$

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MCQ 131 Mark

Tick the correct answer in the following? The sum of all interior angles of a regular polygon is $1080^\circ .$ What is the measure of each of its interior angles?

✓
$135^\circ$
B
$120^\circ$
C
$156^\circ$
D
$144^\circ$

Answer

Correct option: A.

$135^\circ$

$(2n - 4) \times 90 = 1080$
$(2n - 4) = 12$
$2n = 16$
Or $n = 8$
Each interior angle $=180-\frac{360}{\text{n}}$
$=180-\frac{360}{8}$
$=180-45$
$=135^\circ$

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MCQ 141 Mark

Tick the correct answer in the following? The angles of a pentagon are $x^\circ , (x + 20)^\circ , (x + 40)^\circ , (x + 60)^\circ$ and $(x + 80)^\circ .$ The smallest angle of the pentagon is:

A
$75^\circ$
✓
$68^\circ$
C
$78^\circ$
D
$85^\circ$

Answer

Correct option: B.

$68^\circ$

$\therefore (5 - 2) \times 180^\circ - x + x + 20 + x + 40 + x + 60 + x + 80$
$\Rightarrow 540 - 5x + 200$
$\Rightarrow 5x - 340$
$\Rightarrow x - 68^\circ$

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