Question

The angles of a hexagon are x + 10°, 2x + 20°, 2x – 20°, 3x – 50°, x + 40° and x + 20°. Find x. *

3 points

60

70

80

100

​

Answer 1

To find:-

• Value of x.

Solution:-

We know that,

Sum of all angles of hexagon is 720°.

So,

⇒ (x + 10°) + (2x + 20°)+ (2x – 20°)+ (3x – 50°) + (x + 40°) + (x + 20°) = 720°

⇒ x + 10° + 2x + 20° + 2x - 20° + 3x - 50° + x + 40° + x + 20° = 720°

⇒ 10x + 20° = 720°

⇒ 10x = 720° - 20°

⇒ 10x = 700°

⇒x = 700°/10

⇒ x = 70°

Verification:-

⇒ (x + 10°) + (2x + 20°)+ (2x – 20°)+ (3x – 50°) + (x + 40°) + (x + 20°) = 720°

⇒ x + 10° + 2x + 20° + 2x - 20° + 3x - 50° + x + 40° + x + 20° = 720°

⇒ 10x + 20° = 720°

• put x = 70°

⇒ (10×70)° + 20° = 720°

⇒ 700° + 20° = 720°

⇒720° = 720°

Hence, Verified.

Therefore,

Value of x is 70°.