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09 Dec 2023, 20:53
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D
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Difficulty:
65%
(hard)
Question Stats:
50% (01:53) correct
50%
(01:53)
wrong
based on 22
sessions
History
Date
Time
Result
Not Attempted Yet
Find the sum of the 7 angles indicated in the figure A2.
A. 490
B. 510
C. 525
D. 540
E. 565
A. 490
B. 510
C. 525
D. 540
E. 565
Attachments
image0 (5).jpeg [ 988.49 KiB | Viewed 898 times ]
10 Dec 2023, 02:55
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Considering below nomenclature for the solution
image-3.jpg [ 13.82 KiB | Viewed 825 times ]
In △ AEJ : ∠1 + ∠5 + ∠AJE = 180°
=> ∠1 + ∠5 = 180° - ∠AJE ... (1)
In ⬠ BCKLH : ∠2 + ∠3 + ∠CKL + ∠KLH + ∠LHB = 540°
=> ∠2 + ∠3 = 540° - ∠CKL - ∠KLH - ∠LHB ...(2)
In Quadrilateral DFGI : ∠4 + ∠6 + ∠7 + ∠GID = 360°
=> ∠4 + ∠6 + ∠7 = 360° - ∠GID ...(3)
(1) + (2) + (3)
∠1 + ∠5 + ∠2 + ∠3 + ∠4 + ∠6 + ∠7 = 180° - ∠AJE + 540° - ∠CKL - ∠KLH - ∠LHB + 360° - ∠GID
=> Sum of seven angles = 540° + 360° + 180° - ( ∠AJE + ∠CKL + ∠KLH + ∠LHB + ∠GID ) = 540° + 360° + 180° - Sum of angles of ⬠ IJKLH
= 540° + 360° + 180° - 540° = 540°
So, Answer will be D
Hope it helps!
Attachment:
image-3.jpg [ 13.82 KiB | Viewed 825 times ]
In △ AEJ : ∠1 + ∠5 + ∠AJE = 180°
=> ∠1 + ∠5 = 180° - ∠AJE ... (1)
In ⬠ BCKLH : ∠2 + ∠3 + ∠CKL + ∠KLH + ∠LHB = 540°
=> ∠2 + ∠3 = 540° - ∠CKL - ∠KLH - ∠LHB ...(2)
In Quadrilateral DFGI : ∠4 + ∠6 + ∠7 + ∠GID = 360°
=> ∠4 + ∠6 + ∠7 = 360° - ∠GID ...(3)
(1) + (2) + (3)
∠1 + ∠5 + ∠2 + ∠3 + ∠4 + ∠6 + ∠7 = 180° - ∠AJE + 540° - ∠CKL - ∠KLH - ∠LHB + 360° - ∠GID
=> Sum of seven angles = 540° + 360° + 180° - ( ∠AJE + ∠CKL + ∠KLH + ∠LHB + ∠GID ) = 540° + 360° + 180° - Sum of angles of ⬠ IJKLH
= 540° + 360° + 180° - 540° = 540°
So, Answer will be D
Hope it helps!
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