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# In triangle DEF above, what is the value of a in terms of b?

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Math Expert
Joined: 02 Sep 2009
Posts: 53066
In triangle DEF above, what is the value of a in terms of b?  [#permalink]

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02 Sep 2018, 22:40
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Difficulty:

15% (low)

Question Stats:

90% (01:00) correct 10% (00:56) wrong based on 40 sessions

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In triangle DEF above, what is the value of a in terms of b?

A. 115 – b
B. 65 + b
C. 180 – b
D. 115 + b
E. b – 65

Attachment:

image004.jpg [ 3.75 KiB | Viewed 615 times ]

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Re: In triangle DEF above, what is the value of a in terms of b?  [#permalink]

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03 Sep 2018, 01:20
Bunuel wrote:

In triangle DEF above, what is the value of a in terms of b?

A. 115 – b
B. 65 + b
C. 180 – b
D. 115 + b
E. b – 65

Attachment:
image004.jpg

exterior angle = sum of opposite interior angles
a= 65 + b
Math Expert
Joined: 02 Aug 2009
Posts: 7334
Re: In triangle DEF above, what is the value of a in terms of b?  [#permalink]

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03 Sep 2018, 01:23
Bunuel wrote:

In triangle DEF above, what is the value of a in terms of b?

A. 115 – b
B. 65 + b
C. 180 – b
D. 115 + b
E. b – 65

Attachment:
image004.jpg

a is external angle in the smaller triangle on the left side..
And is therefore equal to sum of two opposite internal angles...
So a=65+b

B
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Re: In triangle DEF above, what is the value of a in terms of b?  [#permalink]

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03 Sep 2018, 01:30

Let X be the point at which F makes contact with DE!
Since Angle FXE = a | Angle FXD = 180 - a (Angles in a straight line always have a sum of 180)

In Triangle DFX, the sum of angles is 180 -> $$b + 65 + 180 - a = 180$$ -> $$a = b + 65$$

Therefore, the value of a in terms of b is a = b + 65(Option B)
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Re: In triangle DEF above, what is the value of a in terms of b?  [#permalink]

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11 Sep 2018, 16:14
Bunuel wrote:

In triangle DEF above, what is the value of a in terms of b?

A. 115 – b
B. 65 + b
C. 180 – b
D. 115 + b
E. b – 65

Attachment:
image004.jpg

Since an exterior angle of a triangle (in this case, angle a) is equal to the sum of the two remote interior angles (in this case, angle b and the angle measuring 65 degrees), we see that:

a = 65 + b

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Re: In triangle DEF above, what is the value of a in terms of b?   [#permalink] 11 Sep 2018, 16:14
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