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:
2016-06-17_1624.png
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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