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# What is a in terms of b and y?

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

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Updated on: 13 Sep 2017, 03:27
3
00:00

Difficulty:

55% (hard)

Question Stats:

71% (02:31) correct 29% (02:26) wrong based on 51 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 859 times ]

Attachment:

Untitled2.png [ 25.84 KiB | Viewed 915 times ]

Originally posted by jboog on 13 Sep 2017, 03:18.
Last edited by Bunuel on 13 Sep 2017, 03:27, edited 1 time in total.
Edited the question.
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Posts: 7335
Re: What is a in terms of b and y (exterior/interior angles of a triangle)  [#permalink]

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13 Sep 2017, 03:30
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, 03:42
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, 07:44
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, 08:15
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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What is a in terms of b and y?  [#permalink]

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13 Sep 2017, 13:01
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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Re: What is a in terms of b and y?  [#permalink]

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11 Oct 2018, 02:33
Bunuel 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

Attachment:
Capture (1).JPG

a = x + 90

b = x + y + 15

x = b - y -15

Now substitute the value of x .

a = x + 90

a = b - y - 15 + 90

a = b - y + 75

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

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13 Oct 2018, 17:45
Bunuel 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

Attachment:
Capture (1).JPG

Since a is an exterior angle of the triangle on the left, a = x + 90 or x = a - 90

Since b is an exterior angle of the triangle on the right, b = x + 10 + y + 5 or b = x + y + 15.

Now we can substitute x = a - 90 into b = x + y + 15:

b = a - 90 + y + 15

a + y - 75 = b

a = b - y + 75

Alternate Solution:

Since a and y are supplementary angles, a + y = 180 or a = 180 - y.

Since b is an exterior angle of the triangle on the right, b = x + 10 + y + 5 or b = x + y + 15.

Since x + y + 90 = 180, x + y = 90. Substituting this for the expression for b, we get b = 90 + 15 = 105.

Then, a = 180 - y = 105 + 75 - a = b + 75 - y.

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Re: What is a in terms of b and y?   [#permalink] 13 Oct 2018, 17:45
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