Four adjacent angles are on a line. the measurements of the four angles are four consecutive even numbers. determine the measurements of all four angles.

Since all 4 angles are on a line, we know they must sum to 180 degrees:
.

By definition, for a number to be even, the remainder when it is divided by 2 must be zero (i.e. n%2=0). To ensure this we can incorporate the 2 we need into the number itself by calling our number .

Then to get 4 consecutive even numbers we can start with our first number and count up by 2s:     and .

Now we can sum up our numbers, using the known total:


And the we can solve for 'n'. First group like terms:

Subtract 12 from both sides:

and divide both sides by 8:


Now that we have 'n' we can find our 4 angles:





These are indeed consecutive even (i.e. n/2=0 for all 'n') numbers, just as we wanted.
To check our answer we can make sure they add up to 180:




That checks out so our angles are 42°, 44°, 46° and 48°.