Let the other angle be x.

Other angle = x

Replace the words "the other" by "x"

Replace the words "4 times x" by "4x"

The words "20 degrees less than" before "4x" tells us that we
are to start with 4x and make it 20 degrees less.  To make it
less means to subtract from it.  So we are to make 4x less by
subtracting 20 from it. 

So replace the words "20 degrees less than 4x" by "4x-20".

Replace the word "is" by "="

Now we have

and

Other angle = x

That means




(4x-20) + x = 180
4x - 20 + x = 180
    5x - 20 = 180
         5x = 200
          x = 40

So One angle = 4x-20 = 4(40)-20 = 160-20 = 140°

and

"the other angle" = x = 40° 

Edwin