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28 Sep 2018, 16:14
Kudos
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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:
25%
(medium)
Question Stats:
81% (01:50) correct
19%
(01:29)
wrong
based on 49
sessions
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Not Attempted Yet
In the figure shown, AB=AC and CE=CF. What is the value of x?
(A) 90
(B) 110
(C) 120
(D) 130
(E) 140
Source: https://www.GMATH.net
(Exercise 12 of the Quant Class #02 included in our free test drive!)
Attachment:
GMATH_figure028.gif [ 2.66 KiB | Viewed 1782 times ]
28 Sep 2018, 19:05
Kudos
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fskilnik
Attachment:
GMATH_figure028EDIT (2).jpg [ 19.86 KiB | Viewed 1740 times ]
• Angles opposite congruent sides are congruent
• Vertical angles are congruent
• Angles that are colinear sum to 180°
• The sum of interior angles of a triangle = 180°
Given: ∠ F = 40°
∠ F = ∠ CEF = 40° (angles opposite congruent sides are congruent)
Sum of the two congruent angles
(40° + 40°) = 80°
In ∆ CEF, the third angle,
∠ECF must = (180°- 80°) = 100°
∠ ECF and ∠ ACB, are colinear
∠ ACB must = (180° - 100°) = 80°
∠ACB = ∠ABC = 80° (opposite sides AB = AC)
Vertical angles: ∠CEF = ∠BED
From above ∠CEF = 40° = ∠BED
The two known angles of ∆BDE sum to (40° + 80°) = 120°
Third angle BDE = (180° - 120°) = 60°
Finally, because the angles are colinear: \((x+∠BDE) = 180°\)
\((x+60°)=180°\)
\(x=120°\)
Answer C
30 Sep 2018, 08:49
Kudos
Bookmarks
fskilnik
Dear generis,
Thank you for your excellent (and very detailed) contribution. Kudos!
The "alternate" way, presented in the figures below, has (I believe) one merit:
It takes into account the "exterior angle property", avoiding some intermediate calculations.
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
