There is a circle O with radii A, B, C, and D. CD and AB are chords that are parallel to each other. If Arc BD = 75 and Arc CD equals 90, find angle AOB.

Question

There is a circle O with radii A, B, C, and D. CD and AB are chords that are parallel to each other.  If Arc BD = 75 and Arc CD equals 90, find angle AOB.

anonymous · Answer

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anonymous · Answer

angle BOD is given as 75

By symmetry, angle BOD is the same as AOC, so both are 75.

I think you can add these two angles plus the 90 degree angle, and subtract it all from 360 to get AOB

anonymous · Answer

Thanks! Question why is it that that angle COD and anle AOB are not equal?

anonymous · Answer

They look like that in my (bad) drawing, but they are not actually vertical angles.

anonymous · Answer

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anonymous · Answer

The diagram I'm given in my book, it makes it look like they are  vertical angles, also. This is from barrons regents geometry book.

anonymous · Answer

They do that, I guess, on purpose to see if you are actually figuring it out or just guessing that they look equal.

anonymous · Answer

Sketch a few different circles with different length chords like this, and you can see that the angles won't necessarily be equal.

In fact, the only time they will be equal is if the two chords are equal length, like the top and bottom of a rectangle inside a circle.

anonymous · Answer

Thank you!

anonymous · Answer

Glad to help :)