<span>the 6 exterior measures = a, b, c, d, e, f.
Their sum is 360 degrees.
For each one, the interior angle = 180 - exterior.
So for your problem,
a = 55, b = 60, c = 69, d = 57,
e = (missing one)
f = (remaining one, not given).
Take 55 + 60 + 69 + 57 + e, subtract from 360 to get f.
f = 119 - e.
Then the interior angles are:
125, 120, 111, 123, (180 - e), and (180 - 119 + e) = (61 + e).</span>
I think you're describing the number 0.888... where the 8s will keep
going forever and never end.
Now, I've been around a long time, and worked a lot of math, but
I never knew how to make a fraction out of repeating decimal until
just a short time ago. That's exactly what we need here. Here's
the trick:
-- You have a decimal, with a set of digits ... 1 or 2 or 3 or however many ...
that repeat.
-- Take one complete set of the digits that repeat. Write them
on top of a fraction.
-- On the bottom of the fraction, write the same number of nines
as however many digits are on top.
-- THERE's your fraction that's equivalent to the repeating decimal !
You can go ahead and simplify it if it's possible and you feel like it.
In this problem, the repeating part is only one digit ... the 8 .
Write 8 on top of the fraction. Then write a single 9 on the bottom.
There's your equivalent fraction.
0.888...repeating is equal to 8/9 .
