Bunuel wrote:

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.

Attachment:

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We are given the following diagram:

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.

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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