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Sub 505 (Easy)|   Geometry|      
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Bunuel
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In triangle DEF above, what is the value of a in terms of b? 02 Sep 2018, 23:40
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93% (01:02) correct 7% (00:56) wrong based on 50 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


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B
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In triangle DEF above, what is the value of a in terms of b? 03 Sep 2018, 02:20
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Bunuel

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


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image004.jpg
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exterior angle = sum of opposite interior angles
a= 65 + b
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In triangle DEF above, what is the value of a in terms of b? 03 Sep 2018, 02:23
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Bunuel

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


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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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In triangle DEF above, what is the value of a in terms of b? 03 Sep 2018, 02:30
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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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In triangle DEF above, what is the value of a in terms of b? 11 Sep 2018, 17:14
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Bunuel

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


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image004.jpg
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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

Answer: B
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