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04 Nov 2020, 03:30
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
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92% (02:35) correct
8%
(03:21)
wrong
based on 50
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ABCDE is a regular pentagon. Sides AE and ED of the pentagon are extended as shown to form triangle EFG, which is right-angled at F. Vertices A and C are joined to form the triangle ABC. What is the value of sum (x° + y°)?
A. 30°
B. 45°
C. 54°
D. 60°
E. 72°
Attachment:
1.png [ 17.13 KiB | Viewed 4693 times ]
Updated on: 06 Nov 2020, 12:19
Originally posted by CrackverbalGMAT on 04 Nov 2020, 05:22.
Last edited by CrackverbalGMAT on 06 Nov 2020, 12:19, edited 1 time in total.
Last edited by CrackverbalGMAT on 06 Nov 2020, 12:19, edited 1 time in total.
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Bunuel
Each interior angle of a regular polygon is given by \(\frac{(n - 2)*180}{n}\)
Her n = 5. Therefore each interior angle = \(\frac{(5 - 2)* 180} {5} = 108^o\)
In triangle ABC, BC = AB and therefore \(\angle{BCA} = \angle{BAC} = \frac{180 - 108}{2} = 36\)
x = 36
\(\angle{DEA} = 108\) and therefore \(\angle{GEF} = 180 - 108 = 72\), as the sum of angles on a straight line = 180
In triangle GFE, y + 90 + 72 = 180 since sum of angles of a triangle = 180
Therefore y = 18
x + y = 36 + 18 = 54
Option C
Arun Kumar
04 Nov 2020, 10:34
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Bunuel
each angle of pentagon = 108
FEG = 180 - 108 = 72
y= 18
ABC = 108,
2x= 180 - 108 = 72
x = 36
x + y = 36 + 18 = 54
Answer C
