<p>If the measure of an interior angle of a regular polygon is four times the measure of an exterior angle, how many sides does the polygon have?
A-8
B-9
C-10
D-12
E-15</p>
<p>A trapezoid ACDF, AF is parallel to CD. B is midpoint of AC, and E is the midpoint of DF. If CD=6 and BE=7, what is AF?</p>
<p>A-6
B-7
C-8
D-9
E-10</p>
<p>These questions are from a random SAT Prep Book, so there's no answer to it :(
Please help? I really suck at Geometry :((</p>
<p>Thanks in advance</p>
<p>c. 10 we know that the measure of an exterior angle is 360/n where n is the number of sides
from the problem, we can come up with the equation 180-(360/n)=4(360/n)…divide both sides by four [45-(360/4n)=(360/n)]…add (360/4n or simplified: 90/n) to both sides [45=(360/n)+(90/n)]…add [45=(450/n)]…multiply both sides by n and divide both sides by 45 [n=10]</p>
<p>Is a diagram provided with the trapezoid question?</p>
<p>Another way: you know that the interior angle + the exterior angle = 180. So you need two numbers that have a 4:1 ratio and add up to 180. You can guess and check or you can get the numbers by doing 180/5= 36 (dividing by 5 because a 4:1 ratio means 5 parts total) and then 36<em>1=36 is the smaller, 36</em>4=144 is the larger.</p>
<p>Once you have that the exterior angle is 36, you know there must be 10 sides because the exterior angles always add up to 360.</p>
<p>For trapezoid question,answer is c -8 </p>
<p>Solution:
For trapezoid BE is the median and the length of the median =1/2 (sum of the length of the parallel sides)
BE=7
CD=6
BE=1/2(CD+AF)
7=1/2(6+AF)
14=6+AF
AF=8</p>