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Allushta [10]
3 years ago
15

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:
Anestetic [448]3 years ago
7 0

Answer:

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

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Dmitriy789 [7]

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3 years ago
ILL GIVE BRAINLEST Determine whether the two angles in each figure are complementary, supplementary, or neither
Firdavs [7]

Answer:

Step-by-step explanation:

If the sum of two angles = 180°

Then the pair of angles will be supplementary.

If the sum of two angles = 90°

Then the pair of angles will be complementary.

Sum of angles having measures 98° and 82° = 98° + 82°

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Therefore, both the angles will be supplementary.

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fgiga [73]
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