For a polygon with n sides, the interior angles add up to:
(n - 2) x 180
an octagon has 8 sides:
(8 - 2) * 180 = 6 * 180 = 1080
from the question,1 side measures 2x while 7 sides measure x. this means
7x + 2x = 1080
9x = 1080
x = 1080/9
x = 120°
if x=120°
2x=2(120°)=240°
so, the seven smaller angles are 120°. while the one larger angle is 240°
Answer:
Step-by-step explanation:
Let x represent the measures of the seven same-size angles, and x/2 the measure of the one that is "two times smaller." Their sum is the total measure of angles of an octagon, 6×180° = 1080°. So the equation expressing that is ...
7x + x/2 = 1080
(15/2)x = 1080 . . . . collect terms
x = 1080·(2/15) = 144 . . . . . multiply by the inverse of the coefficient of x
Seven angles are 144° and the eighth is 72°.
