- Exterior angle = 360º ÷ number of sides . Interior angle = 180º - exterior angle . Sum of interior angles = 180 x (number of sides - 2) Example. A regular polygon has an interior angle of 165.6º. How many sides does it have? Answer. Exterior angle = 180 - interior angle = 180 - 165.6 = 14.4º. No. of sides = 360 ÷ exterior angle = 360 ÷ 14.4 = 25
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- If each angle of a triangle is less than the sum of the other two, show that the triangle is acute angled. Answer: Let a triangle ABC having angles . According to exterior angle theorem, Therefore, the given statement is . (xi) An exterior angle of a triangle is greater than the opposite interior angles.
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