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pyth99

Guest

Octagons and Angles

Can someone help me with this problem:

Five of the angles of an octagon haves measures whose sum is 845 degrees.  Of the remaining three angles, two are complementary to each other and two are supplementary to each other.  Find the measures of the three remaining angles.

Thanks,

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Octagons and Angles

The angles of an octagon all add up to (8-2)*180 = 1080.

5 of them add to 845, so the remaining three add to 235. Call these a, b and c.
It doesn't really matter which angles we take to be com/supplementary with each other, so we'll say:

a+b = 90
a+c = 180

We also have that a+b+c = 235.

Putting the first equation into the third one gives that 90+c = 235, and so c = 145.
Similarly with the second equation, we get 180+b = 235 and so b = 55.
Now using this b with the first equation, a+55 = 90 and so a = 35.

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