Question

The angles of a pentagon are x°, (x-5)°, (x+15)°, (3x-44)°and (x-70)°.
Find x°.

Answer 1

x° = 92° if angles of a pentagon are x°, (x-5)°, (x+15)°, (3x-44)°and (x-70)°.

Given:

Angles of a pentagon are x°, (x-5)°, (x+15)°, (3x-44)°and (x-70)°

To Find:

x°

Solution:

Sum of all the angles of a polygon with n sides is given by :

(n - 2) 180°

Pentagon has 5 Side so sum of all the angles of pentagon is:

(5 - 2) 180°  = 540°

Sum of all the given angles of pentagon

= x° + (x-5)° + (x+15)° + (3x-44)° + (x-70)°

= (7x - 104)°

Equate Sum of all the angles with 540° and solve for x

(7x - 104)°= 540°

=> 7x° = 644°

=> x° = 92°

x° = 92° if angles of a pentagon are x°, (x-5)°, (x+15)°, (3x-44)°and (x-70)°.