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# In the regular octagon above, what is x?

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Math Expert
Joined: 02 Sep 2009
Posts: 60473
In the regular octagon above, what is x?  [#permalink]

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15 Nov 2019, 01:38
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Difficulty:

55% (hard)

Question Stats:

53% (02:48) correct 47% (02:03) wrong based on 31 sessions

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In the regular octagon above, what is x?

A. 157.5°
B. 150°
C. 145°
D. 135°
E. 120°

Are You Up For the Challenge: 700 Level Questions

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Math Expert
Joined: 02 Aug 2009
Posts: 8342
In the regular octagon above, what is x?  [#permalink]

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16 Nov 2019, 04:17
Bunuel wrote:

In the regular octagon above, what is x?

A. 157.5°
B. 150°
C. 145°
D. 135°
E. 120°

Are You Up For the Challenge: 700 Level Questions

Attachment:
The attachment Untitled.png is no longer available

Join B and C..
Take$$\triangle ADC......\angle{DAC}=135$$ ( internal angle of octagon) and $$\angle{ADC}=\angle{ACD}=\frac{180-135}{2}=22.5$$( AD and AC are sides of Octagon)
Similarly take Take$$\triangle ADB......\angle{ADB}=135$$ ( internal angle of octagon ) and $$\angle{DAB}=\angle{ABD}=\frac{180-120}{2}=22.5$$( sides of octagon )

Now take $$\triangle {ADO}$$ and $$\triangle {BOC}$$..Both are similar as AD||BC.
Therefore $$\angle{DAB}=\angle{ABC}=22.5$$ and $$\angle{ADC}=\angle{BCD}=22.5$$

Finally take $$\triangle{BOC}$$......Sum of angles = $$x+22.5+22.5=180....x=135$$

D
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Joined: 09 Aug 2017
Posts: 673
Re: In the regular octagon above, what is x?  [#permalink]

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16 Nov 2019, 04:54
1
I think angle DAC is 135 because it octagon.
External angle is 45.

chetan2u wrote:
Bunuel wrote:

In the regular octagon above, what is x?

A. 157.5°
B. 150°
C. 145°
D. 135°
E. 120°

Are You Up For the Challenge: 700 Level Questions

Attachment:
Untitled.png

Join B and C..
Take$$\triangle ADC......\angle{DAC}=120$$ ( internal angle of hexagon) and $$\angle{ADC}=\angle{ACD}=\frac{180-120}{2}=30$$( AD and AC are sides of hexagon)
Similarly take Take$$\triangle ADB......\angle{ADB}=120$$ ( internal angle of hexagon) and $$\angle{DAB}=\angle{ABD}=\frac{180-120}{2}=30$$( sides of hexagon)

Now take $$\triangle {ADO}$$ and $$\triangle {BOC}$$..Both are similar as AD||BC.
Therefore $$\angle{DAB}=\angle{ABC}=30$$ and $$\angle{ADC}=\angle{BCD}=30$$

Finally take $$\triangle{BOC}$$......Sum of angles = $$x+30+30=180....x=120$$

E
Math Expert
Joined: 02 Aug 2009
Posts: 8342
Re: In the regular octagon above, what is x?  [#permalink]

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16 Nov 2019, 05:25
gvij2017 wrote:
I think angle DAC is 135 because it octagon.
External angle is 45.

chetan2u wrote:
Bunuel wrote:

In the regular octagon above, what is x?

A. 157.5°
B. 150°
C. 145°
D. 135°
E. 120°

Are You Up For the Challenge: 700 Level Questions

Attachment:
Untitled.png

Join B and C..
Take$$\triangle ADC......\angle{DAC}=120$$ ( internal angle of hexagon) and $$\angle{ADC}=\angle{ACD}=\frac{180-120}{2}=30$$( AD and AC are sides of hexagon)
Similarly take Take$$\triangle ADB......\angle{ADB}=120$$ ( internal angle of hexagon) and $$\angle{DAB}=\angle{ABD}=\frac{180-120}{2}=30$$( sides of hexagon)

Now take $$\triangle {ADO}$$ and $$\triangle {BOC}$$..Both are similar as AD||BC.
Therefore $$\angle{DAB}=\angle{ABC}=30$$ and $$\angle{ADC}=\angle{BCD}=30$$

Finally take $$\triangle{BOC}$$......Sum of angles = $$x+30+30=180....x=120$$

E

Yes, you are correct. I have answered the question taking it as a hexagon.
Octagon means internal angle is 135 and similarly as the way solves for hexagon it will be 135
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Re: In the regular octagon above, what is x?   [#permalink] 16 Nov 2019, 05:25
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