In a pentagon, the second angle is twice the first but half of the fourth, third angle is three times the first and the fifth angle is 20° less than the fourth. Find all the angles.​

Step-by-step explanation:

Let the first angle be  = x

Given:

           Second angle is twice first = 2x

           Third angle is three times first = 3x

Also given:

  Second angle is half of fourth angle, that is:

 Fifth angle is 20° less than fourth angle, that is:

Sum of interior angles of a polygon with n sides = ( n - 2 ) x 180°

Here n = 5 ,

   therefore sum of interior angles = ( 5 - 2 ) x 180 = 3 x 180 = 540°.

That is ,

             x + 2x + 3x + 4x + ( 4x - 20 )  = 540

                                           14x - 20 = 540

                                                  14x = 540 + 20

                                                  14x = 560

                                                     x = 40