Top Score: QR Test #1 Question #3

[Djdents]

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Can anyone explain this question (attached)

 

[n27s]

Arc will be 360- (100+140) = 120
The angle is 1/2 the measure of the arc so 60.
Note: if the angle was measured from the center of the circle the angle would have been 120.

 

[Ari Rezaei]

The arc of a complete circle is 360. They give you the two other arcs, 100 and 140. Adding these together and subtracting from 360 we get the missing arc that we need, 360 - (100+140) = 120 degrees.

This part is a geometry rule. The missing angle is equal to half of the arc it touches. So the missing angle should be 120/2 = 60 degrees.

Try this. If the angle was expanded outwards a little more so that the arc is 180 (as opposed to the 120 in the problem), you can see that the missing angle must be 90 degrees. But, if the angle was being measured directly from the middle of the circle, the angle would just measure exactly the arc value, 180 degrees.

 

[Djdents]

Thanks guys, got it.