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°.

Answer 2

The measure of the four angles are 42, 44, 46 and 48

Let the smallest angle be x.

Given that the angles are consecutive even numbers, then we have the following equation

x + x + 2 + x + 4 + x + 6 = 180

Collect like terms

x + x + x + x = 180 -2 -4 -6

Evaluate the like terms

4x = 168

Divide both sides by 4

x = 42

The other angles are: x + 2, x + 4 and x + 6

Hence, the measure of the four angles are 42, 44, 46 and 48

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