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प्रश्न
The sum of interior angles of a regular polygon is thrice the sum of its exterior angles. Find the number of sides in the polygon.
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उत्तर
Sum of interior angles = 3 x Sum of exterior angles
Let exterior angle = x
The interior angle = 3x
x + 3x=180°
⇒ 4x = 180°
⇒ x = `180/4`
⇒ x = 45°
Number of sides = `360/45 = 8`
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संबंधित प्रश्न
Fill in the blanks :
In case of regular polygon, with :
| No.of.sides | Each exterior angle | Each interior angle |
| (i) ___8___ | _______ | ______ |
| (ii) ___12____ | _______ | ______ |
| (iii) _________ | _____72°_____ | ______ |
| (iv) _________ | _____45°_____ | ______ |
| (v) _________ | __________ | _____150°_____ |
| (vi) ________ | __________ | ______140°____ |
Find the number of sides in a regular polygon, if its exterior angle is : `1/3` of right angle
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The measure of each interior angle of a regular polygon is five times the measure of its exterior angle. Find :
(i) measure of each interior angle ;
(ii) measure of each exterior angle and
(iii) number of sides in the polygon.
In a regular pentagon ABCDE, draw a diagonal BE and then find the measure of:
(i) ∠BAE
(ii) ∠ABE
(iii) ∠BED
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Calculate the number of sides of a regular polygon, if: the ratio between its exterior angle and interior angle is 2: 7.
Calculate the number of sides of a regular polygon, if: its exterior angle exceeds its interior angle by 60°.
Find number of side in a regular polygon, if it exterior angle is: 36
Which formula correctly represents the sum of interior angles of an n-sided polygon?
