If one angle of a pentagon is 120° and each of the remaining four ang

1.	If one angle of a pentagon is 120° and each of the remaining four angles is x°, find the magnitude of x.
Answer» One angle of a pentagon = 120° Let remaining four angles be x, x, x and x Their sum = 4x + 120° But sum of all the interior angles of a pentagon = (2n – 4) x 90° = (2 x 5 – 4) x 90° = 540° = 3 x 180° = 540° ∴ 4x + 120° = 540° 4x = 540° – 120° 4x = 420 x = (420/4)° ⇒ x = 105° ∴Equal angles are 105° (Each)

If one angle of a pentagon is 120° and each of the remaining four angles is x°, find the magnitude of x.

Answer»

One angle of a pentagon = 120°

Let remaining four angles be x, x, x and x

Their sum = 4x + 120°

But sum of all the interior angles of a pentagon = (2n – 4) x 90°

= (2 x 5 – 4) x 90° = 540°

= 3 x 180° = 540°

∴ 4x + 120° = 540°

4x = 540° – 120°

4x = 420

x = (420/4)° ⇒ x = 105°

∴Equal angles are 105° (Each)