A nonregular hexagon has five exterior angle measures of 55, 60, 69, 57, and 57. What is the measure of the interior angle adjacent to the sixth exterior angle?
2007-10-29 14:34:59 · 5 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
[09]
The sum of the measures of the 5 exterior angles is
55+60+69+57+57
=298degrees
The sixth exterior angle
=360-298
=62 degrees
Therefore the measure of the interior angle adjacent to this exterior angle
=180-62
=118 degrees
2007-10-29 14:42:15 · answer #1 · answered by alpha 7 · 0⤊ 0⤋
im not sure but I think all the exterior angles add up to 360 degrees.
360 - 55 - 60 - 69 - 57 - 57 and u get some number
180 - some number gives you the interior angle.
2007-10-29 14:38:23 · answer #2 · answered by Anonymous · 0⤊ 0⤋
The *exterior* angles in any polygon always add up to 360 degrees.
55 + 60 + 69 + 57 + 57 + x = 360
298 + x = 360
x = 62
So the missing *exterior* angle is 62 degrees.
The interior and exterior angles are always supplementary (add up to 180 degrees).
n + 62 = 180
n = 180 - 62
n = 118
Therefore the *interior* angle will be 118 degrees.
2007-10-29 14:40:49 · answer #3 · answered by Puzzling 7 · 0⤊ 0⤋
55 + 60 + 69 + 57 + 57 = 298
all 6 must total to 360 therefore the 6th is 62
so the interior angle at this vertex is 180 - 62
which is....
118!!!
2007-10-29 14:41:10 · answer #4 · answered by Anonymous · 0⤊ 0⤋
impossible. unless the wording is incorrectly written.
2007-10-29 14:47:34 · answer #5 · answered by Megumi H 3 · 0⤊ 0⤋