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# What is a in terms of b and y?

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Intern
Joined: 12 Nov 2015
Posts: 31
What is a in terms of b and y? [#permalink]

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Updated on: 13 Sep 2017, 04:27
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Difficulty:

45% (medium)

Question Stats:

72% (03:05) correct 28% (03:01) wrong based on 46 sessions

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What is a in terms of b and y?

(A) b + y + 65
(B) b - y + 65
(C) b + y + 75
(D) b - 2y + 45
(E) b - y + 75

I found this question somewhat difficult in translating to b and y format.

Was hoping someone could possibly point me to similar questions as this one to practice.

Thank you!
Attachment:

math pic.JPG [ 25.99 KiB | Viewed 722 times ]

Attachment:

Untitled2.png [ 25.84 KiB | Viewed 778 times ]

Originally posted by jboog on 13 Sep 2017, 04:18.
Last edited by Bunuel on 13 Sep 2017, 04:27, edited 1 time in total.
Edited the question.
Math Expert
Joined: 02 Aug 2009
Posts: 5890
Re: What is a in terms of b and y (exterior/interior angles of a triangle) [#permalink]

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13 Sep 2017, 04:30
1
jboog wrote:
What is a in terms of b and y?

I found this question somewhat difficult in translating to b and y format.

Was hoping someone could possibly point me to similar questions as this one to practice.

Thank you!

Hi..
As you have mentioned it is more to do with exterior angles..

Two equations you get is..
1) a=x+90
2) b=x+10+y+5=x+y+15 OR x=b-y-15

Substitute value of x in equation 1
a=b-y-15+90=b-y+75

E
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Re: What is a in terms of b and y? [#permalink]

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13 Sep 2017, 04:42
Use external angle theorem, then get two equations, substitute value of X with other variable present in other equation.

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Re: What is a in terms of b and y? [#permalink]

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13 Sep 2017, 08:44
jboog wrote:

What is a in terms of b and y?

(A) b + y + 65
(B) b - y + 65
(C) b + y + 75
(D) b - 2y + 45
(E) b - y + 75

I found this question somewhat difficult in translating to b and y format.

Was hoping someone could possibly point me to similar questions as this one to practice.

Thank you!
Attachment:
math pic.JPG

Attachment:
Untitled2.png

We need to use external angles properties : An exterior angle of a triangle is equal to the sum of the opposite interior angles.

Therefore given from the figure;

$$a = x + 90$$ -------- (i)

$$b = (x + 10) + (y + 5)$$

$$b = x + y + 15$$

$$x = b - y - 15$$ --------- (ii)

Substituting value of $$x$$ from (ii) to (i), we get;

$$a = b - y - 15 + 90$$

$$a = b - y + 75$$

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What is a in terms of b and y? [#permalink]

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13 Sep 2017, 09:15
From the first triangle, $$x+y+90 = 180 => x+y = 90$$

From the second triangle, $$(180 - b) + x + 10 + y + 5 = 180$$
Since $$x + y = 90, 180 + 10 + 5 + 90 - b = 180 => b = 105$$

We have been asked to find the value of a(in terms of b and y)
Since the sum of angles in a line is 180, $$a+y = 180$$
Therefore $$a = 180 - y = 105 + 75 - y = b - y + 75$$(Option E)
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Joined: 31 Jul 2017
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What is a in terms of b and y? [#permalink]

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13 Sep 2017, 14:01
Given the first triangle is a right triangle, X and Y can be 45 and 45, or 30 and 60. Either way, plugging those values into the second triangle will net an answer that can be solved by (E).
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What is a in terms of b and y?   [#permalink] 13 Sep 2017, 14:01
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