Question

If the exterior angles of a pentagon are x° 2x° (x+30)°,(x-10)° and (x+40)° find x

a) 30
b) 50
c) 60
d) 80

Answer 1

`\fbox {b) 50}`

Explanation:

The sum of the exterior angles of any polygon (including a pentagon) is equal to 360 degrees.

Then :

⇒ x + 2x + x + 30 + x - 10 + x + 40 = 360

⇒ 6x + 60 = 360

⇒ 6x = 300

⇒ x = 50

Answer 2

`\huge\boxed{\sf x = 50}`

Explanation:

Statement:

• The exterior angles of a pentagon add up 360 degrees.

Given angles:

• x°
• 2x°
• (x+30)°
• (x-10)°
• (x+40)°

Solution:

x + 2x + x + 30 + x - 10 + x + 40 = 360

6x + 60 = 360

Subtract 60 to both sides

6x = 360 - 60

6x = 300

Divide 6 to both sides

x = 300/6

x = 50

`\rule[225]{225}{2}`