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# In the figure above, ACD is a line segment. What is the value of x?

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Math Expert
Joined: 02 Sep 2009
Posts: 55236
In the figure above, ACD is a line segment. What is the value of x?  [#permalink]

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24 Aug 2017, 02:04
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In the figure above, ACD is a line segment. What is the value of x?

(A) 30
(B) 33
(C) 36
(D) 40
(E) 45

Attachment:

2017-08-24_1250_003.png [ 7.68 KiB | Viewed 923 times ]

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Re: In the figure above, ACD is a line segment. What is the value of x?  [#permalink]

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24 Aug 2017, 02:14
18t=180;
t=10.
10t+5t+x=180;
x=30
Ans: A

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Re: In the figure above, ACD is a line segment. What is the value of x?  [#permalink]

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24 Aug 2017, 02:57
Ans : A

ACB+BCD = 180 (Supplementary angles)

10t+8t= 180.
Thus t= 10 degree.

In triangle ABC , x+10t+5t= 180 degree.

Thus substituting values , x= 30 degree
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Re: In the figure above, ACD is a line segment. What is the value of x?  [#permalink]

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24 Aug 2017, 04:54
10T+8T = 180

t = 10

therefore, 5t + 10t + x = 180
substituting the value of t we get x = 30

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Re: In the figure above, ACD is a line segment. What is the value of x?  [#permalink]

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24 Aug 2017, 23:20
∠BCD= ∠ABC + ∠BAC .... ( measure of exterior angle of a triangle is always equal to sum of remote interior angles)
5t + x = 8t
x= 3t

Now in triangle ABC
3t+5t+10t=180
18t=180

x=3t=30.
Hence Answer is A.

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Re: In the figure above, ACD is a line segment. What is the value of x?  [#permalink]

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29 Aug 2017, 16:19
Bunuel wrote:

In the figure above, ACD is a line segment. What is the value of x?

(A) 30
(B) 33
(C) 36
(D) 40
(E) 45

A straight angle has 180 degrees. We can create the following equation:

10t + 8t = 180

18t = 180

t = 10

The interior angles of a triangle sum to 180 degrees. Thus:

x + 5(10) + 10(10) = 180

x + 50 + 100 = 180

x = 30

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Re: In the figure above, ACD is a line segment. What is the value of x?  [#permalink]

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07 Sep 2017, 13:13
1
As per the given diagram :

10t+8t= 180
t = 10

Thus, 10t +5t +x = 180
x = 30

The correct answer is Option A.

Bunuel : please change the OA after review.
Math Expert
Joined: 02 Sep 2009
Posts: 55236
Re: In the figure above, ACD is a line segment. What is the value of x?  [#permalink]

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07 Sep 2017, 14:13
chipsy wrote:
As per the given diagram :

10t+8t= 180
t = 10

Thus, 10t +5t +x = 180
x = 30

The correct answer is Option A.

Bunuel : please change the OA after review.

The OA is A. Edited. Thank you.
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Re: In the figure above, ACD is a line segment. What is the value of x?   [#permalink] 07 Sep 2017, 14:13
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# In the figure above, ACD is a line segment. What is the value of x?

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