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# If BCD is a straight line and angle A = 40°, then angle ACD contains

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Math Expert
Joined: 02 Sep 2009
Posts: 55668
If BCD is a straight line and angle A = 40°, then angle ACD contains  [#permalink]

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05 Mar 2018, 22:03
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Difficulty:

25% (medium)

Question Stats:

78% (01:26) correct 22% (01:50) wrong based on 71 sessions

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If BCD is a straight line and angle A = 40°, then angle ACD contains

(A) 40°

(B) 140°

(C) less than 40°

(D) more than 40°

(E) 100°

Attachment:

2018-03-06_0901.png [ 10.67 KiB | Viewed 1400 times ]

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Math Expert
Joined: 02 Sep 2009
Posts: 55668
Re: If BCD is a straight line and angle A = 40°, then angle ACD contains  [#permalink]

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05 Mar 2018, 22:05
Bunuel wrote:

If BCD is a straight line and angle A = 40°, then angle ACD contains

(A) 40°

(B) 140°

(C) less than 40°

(D) more than 40°

(E) 100°

Attachment:
2018-03-06_0901.png

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If BCD is a straight line and angle A = 40°, then angle ACD contains  [#permalink]

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05 Mar 2018, 23:30
Bunuel wrote:

If BCD is a straight line and angle A = 40°, then angle ACD contains

(A) 40°

(B) 140°

(C) less than 40°

(D) more than 40°

(E) 100°

Attachment:
2018-03-06_0901.png

According to the properties of triangle, angle ACD = 40 + B i.e. angle ACD is definitely more than 40.

To find exact degree of angle ACD, we need either the value of B, or the value of C, which isn't provided in the question.

Also, both 140 & 100 are values which hold true for angle ACD.

So correct Answer is D) more than 40

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If BCD is a straight line and angle A = 40°, then angle ACD contains  [#permalink]

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06 Mar 2018, 00:32
Draw a line parallel to the straight line touching the point A. If A is at one end of the line and F marks the other end, angle ACD = angle FAC (as the two straight line will then be parallel and alternate angles of line AC are equal in measure). Even if you tilt the line AC to vary the angle ACB, the angle ACD = angle FAC will always be more than 40 degree.
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Re: If BCD is a straight line and angle A = 40°, then angle ACD contains  [#permalink]

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06 Mar 2018, 04:44
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1
Bunuel wrote:

If BCD is a straight line and angle A = 40°, then angle ACD contains

(A) 40°

(B) 140°

(C) less than 40°

(D) more than 40°

(E) 100°

Attachment:
2018-03-06_0901.png

Angle ACD is an Exterior Angle of a triangle and the exterior and property of a triangle is as mentioned below.

"An exterior angle of a triangle is equal to the sum of the opposite interior angles"

hence
Angle ACD = 40º + Angle ABC
i.e. Angle ACD must be greater than 40

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Re: If BCD is a straight line and angle A = 40°, then angle ACD contains  [#permalink]

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07 Mar 2018, 09:21
Angle acb is either 90 degrees or more than 90 degrees therefore the answer will be option D
Re: If BCD is a straight line and angle A = 40°, then angle ACD contains   [#permalink] 07 Mar 2018, 09:21
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