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What is the degree measure of angle a in the figure above?

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What is the degree measure of angle a in the figure above?  [#permalink]

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New post Updated on: 25 Jun 2014, 07:55
3
8
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

53% (01:10) correct 47% (00:51) wrong based on 300 sessions

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Image

What is the degree measure of angle a in the figure above?

(1) d + e = 275°
(2) b + c = 295°

Spoiler: :: My take
Should be E. I can create an equation with both 1 and 2 that only includes e (which is also a) but the final step is 180 = 2e +180, so everything collapses...


Attachment:
triangle.jpg
triangle.jpg [ 26.05 KiB | Viewed 11194 times ]

Originally posted by Berbatov on 26 Aug 2011, 01:31.
Last edited by Bunuel on 25 Jun 2014, 07:55, edited 2 times in total.
Renamed the topic, edited the question and added the OA.
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Re: What is the degree measure of angle a in the figure above?  [#permalink]

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New post 26 Aug 2011, 02:57
4
Hello,
I guess its B. Please provide OA

Here's my explanaition

given
b + c = 295
180 - f + 180 - g = 295
360 - (f+g) = 295
360 - (180 -e) = 295
180 + e = 295
e = 115
hence a = 115 (vertically opposite angles)

Hope this helps.

Consider Kudos if You could understand my explanation :-D
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Re: What is the degree measure of angle a in the figure above?  [#permalink]

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New post 26 Aug 2011, 02:59
1
<a = <e
Stmt1: d+e=275
e=275-d
We don't know d. Not Sufficient.

Stmt2: b+c=295
b+f=180
c+g=180
Adding, b+c+f+g=360
295+f+g=360
f+g=65
e+f+g=180
e=180-65= 115
a=115
Sufficient.

OA B
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Re: What is the degree measure of angle a in the figure above?  [#permalink]

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New post 16 Aug 2014, 03:24
We can also use the exterior angle property to solve this question

Statement 1
No matter what we do, we can't solve for a

Statement 2
<b=<e+<g-----------------------(1)
<c=<e+<f------------------------(2)

Combining (1) & (2)
<b+<c=2<e+<f+<g
we know that <b+<c=295
295=2<e+<f+<g
295=<e+180
<e=115=<a (vertical angles)
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Re: What is the degree measure of angle a in the figure above?  [#permalink]

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New post 21 Jul 2015, 23:29
Berbatov wrote:
Image

What is the degree measure of angle a in the figure above?

(1) d + e = 275°
(2) b + c = 295°

Spoiler: :: My take
Should be E. I can create an equation with both 1 and 2 that only includes e (which is also a) but the final step is 180 = 2e +180, so everything collapses...


Attachment:
triangle.jpg



Bunuel...Why cant I draw a ll line to the base of the triangle and have d=e?

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Re: What is the degree measure of angle a in the figure above?  [#permalink]

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New post 22 Jul 2015, 00:50
1
Avinashs87 wrote:
Berbatov wrote:
Image

What is the degree measure of angle a in the figure above?

(1) d + e = 275°
(2) b + c = 295°

Spoiler: :: My take
Should be E. I can create an equation with both 1 and 2 that only includes e (which is also a) but the final step is 180 = 2e +180, so everything collapses...


Attachment:
The attachment triangle.jpg is no longer available



Bunuel...Why cant I draw a ll line to the base of the triangle and have d=e?

Avinash


For angle d to be equal to angle e below red lines must be parallel, which is not possible since we won't have a triangle in this case:
Attachment:
Untitled.png
Untitled.png [ 11.94 KiB | Viewed 8407 times ]


Check this: http://www.mathopenref.com/transversal.html
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Re: What is the degree measure of angle a in the figure above?  [#permalink]

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New post 22 Jul 2015, 02:22
Yeah...My bad. I understand now.
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Re: What is the degree measure of angle a in the figure above?  [#permalink]

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New post 21 Jun 2018, 10:27
jamifahad wrote:
<a = <e
Stmt1: d+e=275
e=275-d
We don't know d. Not Sufficient.

Stmt2: b+c=295
b+f=180
c+g=180
Adding, b+c+f+g=360
295+f+g=360
f+g=65
e+f+g=180
e=180-65= 115
a=115
Sufficient.

OA B


I was about to ask how we knew that b+c = 180
Thanks for the explanation.

Posted from my mobile device
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Re: What is the degree measure of angle a in the figure above?  [#permalink]

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New post 01 Jul 2018, 08:05
MrJglass wrote:
jamifahad wrote:
<a = <e
Stmt1: d+e=275
e=275-d
We don't know d. Not Sufficient.

Stmt2: b+c=295
b+f=180
c+g=180
Adding, b+c+f+g=360
295+f+g=360
f+g=65
e+f+g=180
e=180-65= 115
a=115
Sufficient.

OA B


I was about to ask how we knew that b+c = 180
Thanks for the explanation.

Posted from my mobile device

the sum of the angles in a triangle is 180 degrees. Theorem. If ABC is a triangle then <)ABC + <)BCA + <)CAB = 180 degrees
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Re: What is the degree measure of angle a in the figure above? &nbs [#permalink] 01 Jul 2018, 08:05
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