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3 years ago

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?

Mathematics

1 answer:

bixtya [17]3 years ago

3 0

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°

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$-\frac{7}{8}(-\frac{8}{7})x-\frac{3}{4}=20(-\frac{8}{7})$

Step-by-step explanation:

The complete question in the attached figure

Verify each case

Part 1) we have

$-\frac{7}{8}x-\frac{3}{4}=20$

solve for x

$\frac{7}{8}x=-\frac{3}{4}-20$

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$-\frac{7}{8}x-\frac{3}{4}=20$

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That means, that the equations Part 1) and Part 2) are equivalent

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That means, that the equations Part 1) and Part 3) are equivalent

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