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What is the measure of each interior angle of a regular decagon?

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Math Revolution GMAT Instructor
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What is the measure of each interior angle of a regular decagon?  [#permalink]

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New post 23 Jan 2019, 01:10
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[Math Revolution GMAT math practice question]

What is the measure of each interior angle of a regular decagon?

\(A. 72°\)
\(B. 108°\)
\(C. 120°\)
\(D. 135°\)
\(E. 144°\)

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Re: What is the measure of each interior angle of a regular decagon?  [#permalink]

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New post 23 Jan 2019, 01:17
1
Decagon = 10 sides
Interior angle is given by, 180-360/n = 180-360/10 = 180-36 = 144.

E is the answer.
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Re: What is the measure of each interior angle of a regular decagon?  [#permalink]

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New post 23 Jan 2019, 23:32
MathRevolution wrote:
[Math Revolution GMAT math practice question]

What is the measure of each interior angle of a regular decagon?

\(A. 72°\)
\(B. 108°\)
\(C. 120°\)
\(D. 135°\)
\(E. 144°\)


each interior angle
10 sided
180-360/10 = 144
IMO E
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Re: What is the measure of each interior angle of a regular decagon?  [#permalink]

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New post 23 Jan 2019, 23:44
MathRevolution wrote:
[Math Revolution GMAT math practice question]

What is the measure of each interior angle of a regular decagon?

\(A. 72°\)
\(B. 108°\)
\(C. 120°\)
\(D. 135°\)
\(E. 144°\)


Sum of all angles will be (n-2) * 180

n = 10 here, 8 * 180 = 1440

1440/10 = 144

E
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Re: What is the measure of each interior angle of a regular decagon?  [#permalink]

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New post 25 Jan 2019, 02:31
=>

The sum of all interior angles of n-gon is \((n-2)*180°.\)
A decagon is a \(10\)-gon.
The sum of all interior angles is \((10-2)* 180° = 8*180°.\)
And each interior angle of a regular decagon has measure \(\frac{8*180°}{10} = 8*18° = 144°.\)

Therefore, the answer is E.
Answer: E
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Re: What is the measure of each interior angle of a regular decagon?   [#permalink] 25 Jan 2019, 02:31
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