Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 20 Jul 2019, 11:01 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # In the figure, JKLMNP is a regular hexagon .

Author Message
TAGS:

### Hide Tags

Verbal Forum Moderator V
Status: Greatness begins beyond your comfort zone
Joined: 08 Dec 2013
Posts: 2356
Location: India
Concentration: General Management, Strategy
Schools: Kelley '20, ISB '19
GPA: 3.2
WE: Information Technology (Consulting)
In the figure, JKLMNP is a regular hexagon .  [#permalink]

### Show Tags

1
11 00:00

Difficulty:   35% (medium)

Question Stats: 71% (01:53) correct 29% (02:39) wrong based on 197 sessions

### HideShow timer Statistics In the figure, JKLMNP is a regular hexagon .Find the measure of $$\angle$$ MQN.

A. $$30^{\circ}$$
B. $$45^{\circ}$$
C. $$50^{\circ}$$
D. $$60^{\circ}$$
E. $$75^{\circ}$$

Attachments Geometry_Hexagon.PNG [ 461.86 KiB | Viewed 2998 times ]

_________________
When everything seems to be going against you, remember that the airplane takes off against the wind, not with it. - Henry Ford
The Moment You Think About Giving Up, Think Of The Reason Why You Held On So Long
+1 Kudos if you find this post helpful
Manager  Joined: 15 Feb 2015
Posts: 97
In the figure, JKLMNP is a regular hexagon .  [#permalink]

### Show Tags

5
1
Skywalker18 wrote:
In the figure, JKLMNP is a regular hexagon .Find the measure of $$\angle$$ MQN.

A. $$30^{\circ}$$
B. $$45^{\circ}$$
C. $$50^{\circ}$$
D. $$60^{\circ}$$
E. $$75^{\circ}$$

vinnisatija
Theres a very simple explanation for this question.

Remember the formula for the sum of internal angles of a polygon.

Sum of angles= 180 X (n-2) ; where n= number of sides

In our case ; 180 ( 6-2) = 720.

Now this is a regular hexagon. All the angles are equal and all the sides are also equal.

therefore Each angle = 120

Now consider triangle LMN

we know angle M=120.
Since all the sides are equal, we know this is an isosceles triangle.

2x+120=180
x=30.

So angle L= N= 30.

Similarly, in triangle KLM,

angle k and M = 30.

From what we have proved above,

Angle QMN 120-30 = 90

Now we have angle QMN+ Angle MQN + angle QNM = 180

90+MQN+30=180
MQN=60

Hope its clear. Let me know through the kudos button ##### General Discussion
Intern  Joined: 16 Apr 2015
Posts: 39
Concentration: Operations, Strategy
Schools: UFlorida '18, UFL '17
Re: In the figure, JKLMNP is a regular hexagon .  [#permalink]

### Show Tags

can anyone provide an alternate explanation on this ?
CEO  S
Joined: 20 Mar 2014
Posts: 2620
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44 GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: In the figure, JKLMNP is a regular hexagon .  [#permalink]

### Show Tags

Skywalker18 wrote:
In the figure, JKLMNP is a regular hexagon .Find the measure of $$\angle$$ MQN.

A. $$30^{\circ}$$
B. $$45^{\circ}$$
C. $$50^{\circ}$$
D. $$60^{\circ}$$
E. $$75^{\circ}$$

An interesting question that requires you to be a bit creative with the information that you have been given.

The given polygon is a REGULAR hexagon --> all sides and all angles are equal. Every interior angle of a hexagon = 120 degrees.

As per the attached image, draw a circle around the given hexagon. Thus , now you get equal arcs LM=MN=NP=JP=JK=KL . As there are 6 arcs and all arcs must subtend a total of 360 degrees at the center of the circle ---> each arc subtends 60 degrees at the center.

Additionally, an angle subtended by any arc of a circle at the center = 2* angle subtended by the same arc on the circumference.

Consider triangle QNM,$$\angle{QNM}$$ = angle subtended by LM = 30 degrees (as it is the angle subtended by arc LM on the circumference.)

Similarly, Arcs KJ+JP+PN subtend $$\angle{QMN}$$ on the circumference. ---> $$\angle{QMN} = 90 degrees$$.

Finally, in triangle QMN, $$\angle{QMN} + \angle {QNM} + \angle {MQN} = 180 degrees$$ --->$$\angle {MQN}$$ = 180-30-90 = 60 degrees.

Hope this helps.
Attachments 2015-12-05_10-45-47.jpg [ 12.84 KiB | Viewed 2785 times ]

Manager  Status: 2 months to go
Joined: 11 Oct 2015
Posts: 110
GMAT 1: 730 Q49 V40 GPA: 3.8
In the figure, JKLMNP is a regular hexagon .  [#permalink]

### Show Tags

I think there's an easier way to solve this problem.

As we were saying a regular hexagon has each angle measuring $$120°$$.

Now let's look at the image posted above,
the theorem of vertical and adjacent angle pairs says really simply that opposite angles born from the intersection of two lines must be equal.
Therefore if the angle of the hexagon is $$120°$$ the opposite angle will be $$120°$$ as well,
but we also know that the round angle is 360°, therefore, the sum of the remaining opposite pair must be $$360° - 240° = 120°$$,
and since they are opposite as well they have to be equal -> $$\frac{120°}{2}= 60°$$ Originally posted by DensetsuNo on 20 May 2016, 05:57.
Last edited by DensetsuNo on 20 May 2016, 08:29, edited 1 time in total.
Current Student Joined: 18 Oct 2014
Posts: 830
Location: United States
GMAT 1: 660 Q49 V31 GPA: 3.98
Re: In the figure, JKLMNP is a regular hexagon .  [#permalink]

### Show Tags

1
Since it is a regular hexagon, angles made at dissection point by all diagonals will be equal.

Total number of angles made by all diagonals= 6
Total angle made at dissection point = 360

Any single angle measurement will b = 360/6= 60

_________________
I welcome critical analysis of my post!! That will help me reach 700+
Senior Manager  D
Joined: 25 Dec 2018
Posts: 432
Location: India
Concentration: General Management, Finance
GMAT Date: 02-18-2019
GPA: 3.4
WE: Engineering (Consulting)
Re: In the figure, JKLMNP is a regular hexagon .  [#permalink]

### Show Tags

Skywalker18 wrote:
In the figure, JKLMNP is a regular hexagon .Find the measure of $$\angle$$ MQN.

A. $$30^{\circ}$$
B. $$45^{\circ}$$
C. $$50^{\circ}$$
D. $$60^{\circ}$$
E. $$75^{\circ}$$

do you have easy solution? Re: In the figure, JKLMNP is a regular hexagon .   [#permalink] 09 Jan 2019, 01:33
Display posts from previous: Sort by

# In the figure, JKLMNP is a regular hexagon .  