Question 1123275: 1. The exterior angle of a pentagon are in the ratio 2:1:4:3:5
Find each angel of pentagon?
2. The ratio of an exterior angle and interior angle of a regular polygon is 2:7 find
(1) each exterior angle of the regular polygon
(2) number of sides in the polygon
3. The figure of pentagon represents abcde in which side ab and parallel each other angle b c d 7:3:8 then find
b c d angel?
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13198)   (Show Source):
You can put this solution on YOUR website!
(1) The sum of the exterior angles of any polygon is 360 degrees. Let the measures of those angles be 2x, 1x, 4x, 3x, and 5x, and use the sum of 360 degrees to determine the measure of each exterior angle. Then find the measure of each interior angle knowing that each interior and exterior angle have a sum of 180 degrees.
(2) Find the measure of the exterior and interior angles knowing that they are in the ratio 2:7 and their sum is 180 degrees. Then the number of sides is 360 divided by the measure of each exterior angle.
(3) Your statement of this part of the problem is indecipherable....
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Revision....
Apparently your statement of the third problem got corrupted, making it unreadable.
The condition is that side AB and DE are parallel. That means angles A and E are supplementary. Then, since the 5 angles of the pentagon have a total measure of 540 degrees, angles B, C, and D must have an angle sum of 540-180 = 360 degrees.
With the given ratio of angles B, C, and D, let their measures be 7x, 3x, and 8x. Then
7x+3x+8x = 360
18x = 360
x = 20
And the measures of angle B, C, and D are
B: 7x = 140
C: 3x = 60
D: 8x = 160
Note that the given information does not allow us to determine the measures of angles A and E; we only know that the sum of their measures is 180 degrees.
Answer by ikleyn(52776)  (Show Source):
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