SOLUTION: In a hexagon ABCDEF, angle A and angle B are right angles. If angle C is congruent to angles D,E,F, what is the measure of angle F in degrees

Algebra ->  Polygons -> SOLUTION: In a hexagon ABCDEF, angle A and angle B are right angles. If angle C is congruent to angles D,E,F, what is the measure of angle F in degrees      Log On


   

Question 972272: In a hexagon ABCDEF, angle A and angle B are right angles. If angle C is congruent to angles D,E,F, what is the measure of angle F in degrees
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
the sum of the angles of a hexagon are calculated by the following two equations.

first equation s = (n-2)*180 = 4*180 = 720 degrees.

second equation s = (180 - 360/n) * n = (180 - 360/6) * 6 = (180 - 60) * 6 = 120 * 6 = 720.

the first equation uses the normal equation you should be familiar with.

the second equation takes advantage of the fact that the external angle of a polygon is equal to 360 divided by the number of sides of the polygon and the internal angle of the polygon is the supplement of that.

multiply the internal angle by the number of sides and you get the sum of the internal angles of the polygon.

both formulas get you the same answer as they should.

you now know that the sum of the angles is 720.

you also know that the sum of the two right angles is 180.

subtract 180 from 720 to get 540 which you now know has to be divided evenly by the remaining angles of the hexagon.

540 / 4 = 135.

the remaining 4 angles must be equal to 135 apiece.

2 * 90 + 4 * 135 = 180 + 540 = 720.

135 is your answer for each of angles c, d, e, and f.

your answer should be that angle f is equal to 135 degrees.