00:01
Problem says a polygon has m sides if one of its interior angles is 80 degrees and the other interior angles are each equal to 160 degrees find the value of m so m what they're referencing is the number of sides and then we know that the number of sides is also equal to the number of internal angles so that is what i've written out up here so we know that one of the angles is 80 degrees and that the others are 160.
00:37
So to find the total number of angles, what we're going to do is we're going to do 80 plus this m minus 1 is the total number of angles, the m.
00:56
And then we're subtracting one because we already have the one angle, which is 80.
01:02
So we don't have all of the angles included.
01:06
We're missing one.
01:08
So that's what the minus 1 is times 160, because that is the angle, that is how many degrees each of the other angles are.
01:21
And another way to write this is m minus 2 times 1.
01:26
180 degrees.
01:27
So what we're going to do is we're going to set these two equations equal to each other.
01:34
And that's what i have done right here.
01:38
So to solve this, what we're going to do is we're going to distribute these numbers.
01:46
And we're going to, so for the left side, we're going to multiply 180 by m and 180 by negative 2.
01:56
That down here is how we get 180m minus 360 because 180 times negative 2 is negative 360.
02:08
And we're going to do the same thing for the right side...