[3 marks sum]

Question 13 Marks

Is it possible to have a regular polygon whose exterior angle is : $36^\circ$

Answer

Let no. of. sides $= n$
Each exterior angle $= 36^\circ$
$=\frac{360^{\circ}}{ n }=36^{\circ}$
$\therefore n =\frac{360^{\circ}}{36^{\circ}}$
$n = 10$
Which is a whole number.
Hence, it is not possible to have a regular polygon whose each exterior angle is $36^\circ .$

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Question 23 Marks

Is it possible to have a regular polygon whose exterior angle is $: 100^\circ$

Answer

Let no. of. sides $= n$
Each exterior angle $= 100^\circ$
$=\frac{360^{\circ}}{ n }=100^{\circ}$
$\therefore n =\frac{360^{\circ}}{100^{\circ}}$
$n =\frac{18}{5}$
Which is not a whole number.
Hence, it is not possible to have a regular polygon whose each exterior angle is $100^\circ .$

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Question 33 Marks

Is it possible to have a regular polygon whose interior angle is: 135°

Answer

No. of. sides = n
Each interior angle = 135°
$\therefore \frac{(2 n -4) \times 90^{\circ}}{ n }=135^{\circ}$
180n - 360° = 135n
180n - 135n = 360°
$n =\frac{360^{\circ}}{45^{\circ}}$
n = 8
Which is a whole number.
Hence, it is possible to have a regular polygon whose interior angle is 135°.

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Question 43 Marks

Find the number of sides in a regular polygon, if its interior angle is: 150°

Answer

Let no.of.sides of regular polygon be n.
Each interior angle = 150°
$\therefore \frac{(2 n -4) \times 90^{\circ}}{ n }=150^{\circ}$
180n - 360° = 150n
180n - 150n = 360°
30n = 360°
n = 12

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Question 53 Marks

Find the number of sides in a regular polygon, if its interior angle is: 160°

Answer

Let no.of.sides of regular polygon be n.
Each interior angle = 160°
$\therefore \frac{ n -2}{ n } \times 180^{\circ}=160^{\circ}$
180n - 360° = 160n
180n - 160n = 360°
20n = 360°
n = 18

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Question 63 Marks

One angle of a quadrilateral is 90° and all other angles are equal ; find each equal angle.

Answer

Let the angles of a quadrilateral be x°,
x°, x° and 90°
∴ Sum of interior angles of quadrilateral = 360°
⇒ x° + x° + x° + 90° = 360°
⇒ 3x° = 360° - 90°
$\Rightarrow x=\frac{270^{\circ}}{3}$
⇒ x = 90°

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Question 73 Marks

If all the angles of a hexagon are equal, find the measure of each angle.

Answer

No. of sides of hexagon, n = 6
Let each angle be = x°
Sum of angles = 6x°
(n – 2) x 180° = Sum of angles
(6 – 2) x 180° = 6x°
4 x 180 = 6x
$x=\frac{4 \times 180}{6}$
x = 120°
∴ Each angle of hexagon = 120°

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Question 83 Marks

Find the number of sides in a polygon if the sum of its interior angle is $: 1620^\circ$

Answer

Let no. of sides $= n$
$\therefore $Sum of angles of polygon $= 1620^\circ$
$\therefore (2n - a) \times 90^\circ = 1620^\circ$
$\Rightarrow 2( n -2)=\frac{1620^{\circ}}{90^{\circ}}$
$\Rightarrow n -2=\frac{1620^{\circ}}{2 \times 90^{\circ}}$
$\Rightarrow n - 2 = 9$
$\Rightarrow n = 9 + 2$
$\Rightarrow n = 11$

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Question 93 Marks

Find the sum of interior angle of a polygon with: 16 sides

Answer

16 sides
No. of sides n = 16
∴ Sum of interior angles of polygon = (2n – 4) x 90°
= (2 x 16 – 4) x 90°
= (32 – 4) x 90° = 28 x 90°
= 2520°

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MATHS [3 marks sum]

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