DS: What does angle BAO = ?

[leslie]

Set up: Draw a Semi-circle with "O" as the Center point. The right-most point is "D." Draw a line (about 45 degree angle) from "O" to the edge of the circle and label it "B" (so OB is a radius of the circle). Draw another line that is about 100 degrees from "O" to "C" (so we have another radius). Next, extend the base of the semi-circle out to the left and label the end of this "A." Finally, draw a line from "A" to "C" that goes through point "B."

Given: The problem tells you that Circle "O" is a semi-circle with O at the center and that line segment AB = line segment OC

Question: What is the measure of Angle BAO??

1) Angle COD = 60 degrees
2) Angle BCO = 40 degrees

[josh_rider23]

Here is the picture of the problem. I know it has to do with external angles but I can't get why (1) is sufficient just yet.

[josh_rider23]

Okay, this took longer than expected but helped to strengthen some of the triangle rules learned in the course. This problem deals with the exterior angle rule in the geometry book (Ch 4 pg 58) and supplementary angles.

(1) COD is 60, you all ready know that OB and OC are equal because they are both radii of the circle. I labeled angles CBO and BCO s. Since it is given that OC is equal to AB you know that AB is also then equal to OB. So I labeled BAO and AOB both x since they are equal due to the opposite sides being equal. By the rule of exterior angles of a triangle x + x = s, so 2x = s. I labeled angle BOC t. x+t = 120 (180 - COD (60) = 120). So for the larger triangle I have the equation x + s + x+t = 180. I substitute 120 for x+t and 2x for x which gives me x + 2x + 120 = 180. Subtract 120 from both sides and you get 3x = 60, so x = 20, SUFFICIENT.

(2) BCO is 40. Using the same descriptors for angles I have and utilizing again the exterior angles rule I have x + x = s so 2x = 40, x = 20, SUFFICIENT.

Answer D.

[nisarg]

Thanks Josh! This stumped me for quite some time!

[RonPurewal]

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