Question

Two angles of a polygon are right angles and the remaining are 120° each. Find the number of sides in it.

Answer 1

Let the 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 = `(180"n" - 540)/("n" - 2)`

∴ `(180 "n" - 540)/("n" - 2) = 120°`

180n - 540 = 120n - 240

180n - 120n = - 240 + 540

60n = 300

n = `300/60`

n = 5