<p>After reading the answer explanation I still can't seem to understand how to solve this question:</p>
<p>Crazybandit
"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><a href=“http://talk.collegeconfidential.com/sat-preparation/753797-math-help-january-2006-sat-question.html[/url]”>http://talk.collegeconfidential.com/sat-preparation/753797-math-help-january-2006-sat-question.html</a></p>
<p>This problem looks hard, but you have to recognize that the shape you see is a trapezoid - and that’s a four sided figure. Since the big shape (the shape you can’t see) is equilateral, all the angles must be the same. You are given that x + y = 80, so to find out one interior angle, first do 360-80 , (since a four sided figure has angles that add up to 360), then divide it by two - since all the angles must be the same. You get 140 as your answer. Now, to find out how many sides it is, you must use the formula 180(n-2) where n is the number of sides. This will give you the sum of the angles of the shape with the number of sides you put in. You know it can’t be a square or a triangle, (or maybe even a pentagon) just from how it looks, so start from six.
180(6-2)=720/6=120. (We’re looking for 140, so this isn’t it)
180(7-2)=900/7=128.5714…
180(8-2)=1080/8=135
180(9-2)=1260/9=140 (This is what we got as our answer for the interior angle of the shape, so 9 is our answer)</p>
<p>thanks so much this was really helpful! Took me a while even with your explanation but now i have a good understanding of it. :)</p>