<p>I was taking a practice test and I tried this problem (link below) and skipped it after 1 min and 30 sec of no answer. When reviewing my answers, I still couldn't figure it out. Could you geniuses help me, please?? :)
Thanks!
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<p>This question was asked previously many times…
i take no credit for this but i found this helpful</p>
<p>The shown figure is a quadrilateral (4 sides), so the sum of all its angles’ measures is 360 degrees.</p>
<p>x+y = 80
So the sum of the other 2 angles’ measures is 360 - 80, or 280.
Since the other 2 angles have equal measures (as stated in the problem), the measures must be 140.</p>
<p>DOING IT BY HAND:
Regular 3-sided shapes have 60 degree angles - 180 in total
Regular 4-sided shapes have 90 degree angles - 360 in total
Regular 5-sided shapes have ___ degree angles - 540 in total
Regular 6-sided shapes have ___ degree angles - 720 in total
Regular 7-sided shapes have ___ degree angles - 900 in total
Regular 8-sided shapes have ___ degree angles - 1080 in total
Regular 9-sided shapes have ___ degree angles - 1260 in total</p>
<p>140 is the total divided by the number of sides (1260/9), so the answer is 9 sides</p>
<p>You keep adding 180 as the total number of sides increases by 1</p>
<p>DOING IT BY EQUATION:
sum of all angles’ measures =180(n-2), where n = number of sides
180(3-2)=180
180(4-2)=360
180(5-2)=540
180(6-2)=720
180(7-2)=900
180(8-2)=1080
180(9-2)=1260</p>
<p>9 angles of 140 degrees each = 1260</p>
<p>Got it! Thanks a bunch! :)</p>
<p>A faster way to do it would be to use the equation for regular polygons:
180(n-2)=total # of angles
where n is the number of sides
And the total number of angles is equal to the number of sides multiplied by the angle of each side (call x the measure of each interior angle, and so it would be xn)</p>
<p>From x + y = 80, you can then figure out that each angle is 140 degrees.
Then just plug into the equation
180(n-2)=140n
180n-360=140n
40n=360
n=9
So there are 9 sides.</p>
<p>I hope that made sense… but yeah equations save so much time lol.</p>
<p>180(n-2)= the sum of the measurement of each angle, not the total # of angles.</p>
<p>An easier way would be, after figuring out that one angle is 140 degrees:</p>
<p>The “outer angle”, or the angle needed to make it a straight line (180) is 40. All closed polygons have a total “outer angle” of 360. So to find how many angles it has, all you do is 360/40=9. I even drew you a diagram :D</p>
<p>[imgur:</a> the simple image sharer](<a href=“http://imgur.com/UIR1X]imgur:”>Imgur: The magic of the Internet)</p>