In the figure shown, point O is the center of the semicircle and points B, C, and D lie on the semicircle. If the length of line segment AB is equal to the length of line sement OC, what is the degree measure of angle BAO?
(1) The degree measure of angle COD is 60.
(2) The degree measure of angle BCO is 40.
It is given that AB=OC.
Since OC and OB are both radii, OC=OB.
Thus:
EVALUATE THE EASIER STATEMENT FIRST.
Since statement 2 gives information about one of the equal angles, start with statement 2.
Statement 2: The degree measure of angle BCO is 40.
The result is the following combination of angles:
Thus, angle BAO = 20.
SUFFICIENT.
Statement 1: The degree measure of angle COD is 60.
In the combination of angles yielded by statement 2, angle COD = 60.
Thus, statement 1 implies the same combination of angles as does statement 2.
SUFFICIENT.
The correct answer is
D.
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