Question

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.

Answer 1

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

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 $2n$.

Then to get 4 consecutive even numbers we can start with our first number and count up by 2s:    $2n, 2n+2, 2n+4$ and $2n+6$ .

Now we can sum up our numbers, using the known total:
$180=2n+(2n+2)+(2n+4)+(2n+6)$

And the we can solve for 'n'. First group like terms:
$180=8n+12$
Subtract 12 from both sides:
$168=8n$
and divide both sides by 8:
$n=21$

Now that we have 'n' we can find our 4 angles:
$2n=2(21)=42$
$2n+2=2(21)+2=44$
$2n+2=2(21)+4=46$
$2n+2=2(21)+6=48$

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:

$180=42+44+46+48$
$180=180$

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