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

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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GMAT 1: 760 Q51 V42
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What is the measure of each interior angle of a regular decagon?  [#permalink]

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23 Jan 2019, 01:10
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15% (low)

Question Stats:

80% (00:53) correct 20% (00:48) wrong based on 39 sessions

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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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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" NUS School Moderator Joined: 18 Jul 2018 Posts: 1028 Location: India Concentration: Finance, Marketing WE: Engineering (Energy and Utilities) Re: What is the measure of each interior angle of a regular decagon? [#permalink] ### Show Tags 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. _________________ Press +1 Kudos If my post helps! GMAT Club Legend Joined: 18 Aug 2017 Posts: 4976 Location: India Concentration: Sustainability, Marketing GPA: 4 WE: Marketing (Energy and Utilities) Re: What is the measure of each interior angle of a regular decagon? [#permalink] ### Show Tags 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 _________________ If you liked my solution then please give Kudos. Kudos encourage active discussions. Director Joined: 09 Mar 2018 Posts: 997 Location: India Re: What is the measure of each interior angle of a regular decagon? [#permalink] ### Show Tags 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 _________________ If you notice any discrepancy in my reasoning, please let me know. Lets improve together. Quote which i can relate to. Many of life's failures happen with people who do not realize how close they were to success when they gave up. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7999 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: What is the measure of each interior angle of a regular decagon? [#permalink] ### Show Tags 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 _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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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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