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655-705 (Hard)|   Geometry|      
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Bunuel
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What is the measure of an angle of a regular seven-point star? 04 Dec 2020, 09:45
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65% (hard)

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53% (02:14) correct 47% (02:26) wrong based on 64 sessions

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What is the measure of an angle marked with ? of a regular seven-point star shown above?

A. 90/7
B. 120/7
C. 180/7
D. 240/7
E. 540/7

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Find an angle of a regular seven-point star.
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sahuayush
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What is the measure of an angle of a regular seven-point star? 04 Dec 2020, 10:14
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Bunuel, are the options provided correct?

My answer is coming to 540/7, for the angle at the vertex of the star.

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What is the measure of an angle of a regular seven-point star? 04 Dec 2020, 11:38
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sahuayush
Bunuel, are the options provided correct?

My answer is coming to 540/7, for the angle at the vertex of the star.

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IMHO (C) 180/7
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What is the measure of an angle of a regular seven-point star? Updated on: 12 Dec 2020, 04:17
Originally posted by sahuayush on 04 Dec 2020, 11:42.
Last edited by sahuayush on 12 Dec 2020, 04:17, edited 1 time in total.
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What is the measure of an angle of a regular seven-point star? 04 Dec 2020, 16:04
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The central angle is 360/7 so it has to be 540/7.

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What is the measure of an angle of a regular seven-point star? 11 Dec 2020, 20:27
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Bunuel, can you post how you arrived at the solution?

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What is the measure of an angle of a regular seven-point star? 12 Dec 2020, 04:27
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@chetan2u can you share the explanation?

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What is the measure of an angle of a regular seven-point star? 15 Dec 2020, 21:38
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I need answer explanation.
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What is the measure of an angle of a regular seven-point star? 20 Dec 2020, 22:15
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CrackVerbalGMAT can you help with solution here?
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What is the measure of an angle of a regular seven-point star? 21 Dec 2020, 02:39
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Hi Bunuel, the answer which I'm getting is 540/7.


Please refer to the diagram below. A regular star polygon should be like this.


There are 7 equal arcs on the circle. arc AB = arc BC = arc CD = arc DE = arc EF = arc FG = arc GA


\(\angle{\alpha} = \frac{1}{2} * arc \space FEDC\)


Arc FEDC = arc FE + arc EB + arc BC = 3/7 th of the circle = 3/7 * 360 = 1080/7

Therefore \(\alpha = \frac{1}{2} * \frac{1080}{7} = \frac{540}{7}\)

Option E

Arun Kumar
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What is the measure of an angle of a regular seven-point star? 21 Dec 2020, 07:54
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CrackVerbalGMAT
Hi Bunuel, the answer which I'm getting is 540/7.


Please refer to the diagram below. A regular star polygon should be like this.


There are 7 equal arcs on the circle. arc AB = arc BC = arc CD = arc DE = arc EF = arc FG = arc GA


\(\angle{\alpha} = \frac{1}{2} * arc \space FEDC\)


Arc FEDC = arc FE + arc EB + arc BC = 3/7 th of the circle = 3/7 * 360 = 1080/7

Therefore \(\alpha = \frac{1}{2} * \frac{1080}{7} = \frac{540}{7}\)

Option E

Arun Kumar
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How did u come to- angle a= 1/2 * arc fedc? Is there any formulae?

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What is the measure of an angle of a regular seven-point star? 21 Dec 2020, 07:58
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Hea234ven

Angle subtended by an arc/chord at the center is double of the angle subtended by the same arc/chord at the circumference.
Sorry can't post picture. You can google it.
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What is the measure of an angle of a regular seven-point star? 22 Dec 2020, 05:08
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How did u come to- angle a= 1/2 * arc fedc? Is there any formulae?

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There are a couple of equations based on the arc angle.

The simplest is that the arc angle is equal to the central angle subtended by the ends of the arc at the center.

Now this gets related to the property of the chord, where the the angle subtended by the chord at the center, is twice the angle subtended by the same chord at the circumference.

Based on this, the arc angle is twice the angle made by the ends of the arc at the circumference.


Hope this helps

Arun Kumar
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