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18 Jun 2019, 00:49
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
72% (02:34) correct
28%
(02:59)
wrong
based on 217
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Date
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Not Attempted Yet
In the diagram, BC = CD = BD, angle FDE = 40°, angle EFD = 75°, and line BG is parallel to line DF. What is the measure of angle A in degrees?
A. 25
B. 35
C. 45
D. 55
E. 65
Attachment:
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18 Jun 2019, 01:30
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Given info:
1) BC = CD = BD
2) angle FED = 40
3) angle EFD = 75
4) BG || DF
Using (1), angles cbd=bcd=bdc=60
Using (2) and (4), and applying concept of Vertically opposite angles:
angle D made by line segment CD is 40.
Angle between extended DF and BD is 60+40 = 100
Applying sum of interior angles on same transverse is 180
Therefore, upper angle B and D sum to 180
angle B + D = 180
=> B= 180-100 = 80
Now, angle B (made by extended line segment BG and CB):
= 80-60 = 20
Again, applying vertically opposite angles:
angle ABG = 20
From (3) and (4);
angle DFE = BGF = 75
angle BGA = 180 - 75 = 105
therefore, angle BAG = 180 - 105 - 20 = 55
Option D as correct answer
1) BC = CD = BD
2) angle FED = 40
3) angle EFD = 75
4) BG || DF
Using (1), angles cbd=bcd=bdc=60
Using (2) and (4), and applying concept of Vertically opposite angles:
angle D made by line segment CD is 40.
Angle between extended DF and BD is 60+40 = 100
Applying sum of interior angles on same transverse is 180
Therefore, upper angle B and D sum to 180
angle B + D = 180
=> B= 180-100 = 80
Now, angle B (made by extended line segment BG and CB):
= 80-60 = 20
Again, applying vertically opposite angles:
angle ABG = 20
From (3) and (4);
angle DFE = BGF = 75
angle BGA = 180 - 75 = 105
therefore, angle BAG = 180 - 105 - 20 = 55
Option D as correct answer
18 Jun 2019, 01:44
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Bunuel
Find Angle E using sum of angles in a triangle rule = E=65.
angle C=60 as CBD is equilateral triangle (from stem: BC = CD = BD)
So using sum of angles in a triangle rule ACE arrive at angle A 60+65+A=180; A=55 IMO D
+KUDOS, if you like the answer.
