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?

Answers

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°

7 of the angles measure 144 degrees each and one angle measures 72 degrees

Step-by-step explanation:

Let

x -----> represent the measures of the seven same-size angles,

x/2 ----> represent the measure of the one that is "two times smaller."

we know that

The sum of internal angles of a polygon can be calculated as:

S=180^o(n-2)

where

n is the number of sides of the polygon

In this case

n=8 (octagon)

substitute

S=180^o(8-2)=1,080^o

so

The linear equation that represent this problem is

\frac{x}{2}+7x=1,080

solve for x

\frac{15x}{2}=1,080\\\\15x=2,160\\\\x=144^o

so

\frac{x}{2}=72^o

therefore

7 of the angles measure 144 degrees each and one angle measures 72 degrees

7 angles measure 144° each1 angle measures 72°

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°.

Measure of 7 angles is 144 degrees each and measure of 8th angle is 72 degrees.

Step-by-step explanation:

An octagon is an 8-sided polygon. We are given that 7 angles of the octagon have the same measure while one angle is 1/2 times (i.e. half of the other angles). So if each of the 7 angles measure x degrees, the measure of 8th angles would be x/2 degrees.

The sum of internal angles of a polygon can be calculated as:

180(n-2), where n is the number of sides of the polygon. So for an octagon n=8, therefore the sum of internal angles of octagon would be:

180(8-2)= 180 x 6 = 1080 degrees.

We can write the equation as:

Sum of internal angles of octagon = 1080

7x + \frac{x}{2}  = 1080\\\\\frac{15x}{2}=1080\\\\15x=2160\\\\ x=144

This means, 7 of the angles measure 144 degrees and one angle measures 144/2 = 72 degrees.



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