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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 interior angle is: 135°
Is it possible to have a regular polygon whose interior angle is:
138°
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What is the measure of each interior angle of a regular hexagon?
A regular polygon has each exterior angle measuring 40°. How many sides does it have?
What is the sum of all exterior angles of any regular polygon?
