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Two angles of a polygon are right angles and the remaining are 120° each.
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asked May 27, 2019 in Class VIII Maths by muskan15 (-3,443 points)
Two angles of a polygon are right angles and the remaining are 120° each. Find the number of sides in it.
understanding shapes (including polygons)
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answered May 27, 2019 by navnit40 (-4,939 points)
Let number of sides = n
Sum of interior angles = (n – 2) × 180°
= 180n – 360°
Sum of 2 right angles = 2 × 90°
= 180°
∴ Sum of other angles = 180n – 360° – 180°
= 180n – 540
No. of vertices at which these angles are formed = n – 2
∴ Each interior angle = (180n – 540)/(n – 2)
∴ (180n – 540)/(n – 2) = 120°
180n – 540 = 120n - 240
180n – 120n = -240 + 540
60n = 300
n = 300/60
n = 5