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In the figure above, point D is on AC. What is the degree measure of

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In the figure above, point D is on AC. What is the degree measure of [#permalink]

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In the figure above, point D is on AC. What is the degree measure of ∠BAC?

(1) The measure of ∠BDC is 60°
(2) The degree measure of BAC is less than the degree measure of BCD.


[Reveal] Spoiler:
Attachment:
2016-06-17_1624.png
2016-06-17_1624.png [ 27.72 KiB | Viewed 7862 times ]
[Reveal] Spoiler: OA

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Re: In the figure above, point D is on AC. What is the degree measure of [#permalink]

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New post 17 Jun 2016, 06:05
The diagram is not clear is 20 the angle measure of ABD or length of BD?
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Re: In the figure above, point D is on AC. What is the degree measure of [#permalink]

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Re: In the figure above, point D is on AC. What is the degree measure of [#permalink]

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New post 17 Jun 2016, 06:19
Thanks. Answer is A
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Re: In the figure above, point D is on AC. What is the degree measure of [#permalink]

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Case1 : angle BDC = 60 deg

Angle BDC + Angle BDA = 180 degree ( as points ADC form a straight line )

If angle BDC = 60.
Then angle BDA = 180 - 60 =120

The sum of the angles of triangle ABD = 180 degrees.

Angle BDA + Angle ABD + angle BAD = 180 degree

I.e. 120 + 20 + angle BAD = 180 degree.

Angle BAD = angle BAC = 40 degs

Case 2 : clearly insufficient

Therefore A is the correct answer.

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Re: In the figure above, point D is on AC. What is the degree measure of [#permalink]

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New post 18 Jun 2016, 03:52
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IMO A
1).bdc is known
therefore bda=180-bdc
dba=20
so bda+dba+dab=180.
sufficient
2)BCA<BDC
this doesnit give us any information
Insufficient
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Re: In the figure above, point D is on AC. What is the degree measure of [#permalink]

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New post 16 Aug 2016, 14:27
Bunuel wrote:
Image
In the figure above, point D is on AC. What is the degree measure of ∠BAC?

(1) The measure of ∠BDC is 60°
(2) The degree measure of BAC is less than the degree measure of BCD.


[Reveal] Spoiler:
Attachment:
2016-06-17_1624.png

Figure appears to be mirror-image. Could you please correct it
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In the figure above, point D is on AC. What is the degree measure of [#permalink]

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Bunuel wrote:
Image
In the figure above, point D is on AC. What is the degree measure of ∠BAC?

(1) The measure of ∠BDC is 60°
(2) The degree measure of BAC is less than the degree measure of BCD.

[Reveal] Spoiler:
Attachment:
2016-06-17_1624.png


We are given the following diagram:

Image

We need to determine the degree measure of ∠BAC, which is also the degree measure of ∠BAD.

Statement One Alone:

The measure of ∠BDC is 60°.

We can fill the above information into our diagram.

Image

Since ∠ADB and ∠BDC are supplementary, their total degree measurement is equal to 180.

Thus, m∠ADB = 180 – 60 = 120 degrees.

Since we have 2 of the 3 angles in triangle ABD, we can determine the measure of ∠BAC:

m∠BAC = 180 – 120 – 20 = 40 degrees.

Statement one alone is sufficient to answer the question. We can eliminate answer choices B, C, and E.

Alternate solution:

We can see that ∠ADB is an exterior angle of triangle ABD, and it is equal to the sum of the measures of ∠BAD and ∠ABD (recall that the measure of an exterior angle of a triangle is the sum of the measures of the two remote interior angles).

Therefore, m∠BAD = m∠ADB - m∠ABD = 60 - 20 = 40 degrees.

Statement Two Alone:

The degree measure of ∠BAC is less than the degree measure of ∠BCD.

Knowing that the measure of ∠BAC is less than the measure of ∠BCD does not allow us to determine the measure of ∠BAC. Statement two is not sufficient.

Answer: A
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Re: In the figure above, point D is on AC. What is the degree measure of [#permalink]

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Re: In the figure above, point D is on AC. What is the degree measure of   [#permalink] 13 Mar 2018, 03:30
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