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In the regular octagon above, what is x?

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In the regular octagon above, what is x?  [#permalink]

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New post 15 Nov 2019, 01:38
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A
B
C
D
E

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  55% (hard)

Question Stats:

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

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

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New post 16 Nov 2019, 04:17
Bunuel wrote:
Image
In the regular octagon above, what is x?

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


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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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Re: In the regular octagon above, what is x?  [#permalink]

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

chetan2u wrote:
Bunuel wrote:
Image
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
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Re: In the regular octagon above, what is x?  [#permalink]

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

chetan2u wrote:
Bunuel wrote:
Image
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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