Regular polygon X has r sides, and each vertex has an angle measure of s, an integer. If regular polygon Q has r/4 sides, what is the greatest possible value of t, the angle measure of each vertex of polygon Q?
A. 2
B. 160
C. 176
D. 178
E. 179
The OA is C.
Please, can any expert assist me with this PS question? I don't have it clear and I appreciate if any explain it for me. Thanks.
Regular polygon X has r sides, and each vertex has...
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If we want to find the maximum possible angle measure for the interior angles of Q, we first need to find the max possible angle measure for X, as Q will have 1/4 as many sides as X.LUANDATO wrote:Regular polygon X has r sides, and each vertex has an angle measure of s, an integer. If regular polygon Q has r/4 sides, what is the greatest possible value of t, the angle measure of each vertex of polygon Q?
A. 2
B. 160
C. 176
D. 178
E. 179
The OA is C.
Please, can any expert assist me with this PS question? I don't have it clear and I appreciate if any explain it for me. Thanks.
Equation for finding the sum of all interior angles of a polygon with 'n' sides: (n-2) * 180
Equation for finding the measure of each interior angle of a regular polygon with 'n' sides: (n-2)*180/n
If the interior angles of X are integer values, then the greatest possible measure of each angle would be 179 degrees. (180 would be a straight line, and thus not a polygon.)
To find the number of sides of a polygon with interior angles of 179, simply set the above equation to 179:
(n-2)*180/n = 179
(n-2) *180 = 179n
180n - 360 = 179n
-360 = -n
n = 360
So X can have at most 360 sides.
If Q has 1/4 the number of sides as X, then Q, at most, can have 360/4= 90 sides.
If n = 90, each interior angle would be (90-2)*180/90 = 88*180/90 = 88*2 = 176. The answer is C