Question

The measure of one angle of an octagon is two times smaller that of the other seven angles. What is the measure of each angle?

Answer 1

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 2

• 7 angles measure 144° each
• 1 angle measures 72°

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°.