Question

Solve the problem below. Please explain how.

Answer 1

Fun fact. In circles, the angle from the center of the circle to two points on the circle is equal to twice the angle from any point on the circle's larger arc to the same two points.

Answer 2

Wouldn't the angle BOA be 180 - 60 degrees or 120 degrees. we know that angle BAO is equal to angle OBA and are 30 degrees each thus angle BAC is also 30 degrees.

Answer 3

I still don't understand it, but thank you.

Answer 4

Here is the basis of my reasoning. Segment OA is a line segment passing through the center of the circle thus at the center the angle AOC (straight line) is 180 degrees. Do you agree with that?

Answer 5

If you can agree with that premise we then know that the sum of angle COA (60 degrees) and angle BOA is 180 degrees.

Answer 6

i got it now, thank you for explaining it for me! would you mind helping me understand a few other problems?

Answer 7

If they are within my realm of understanding, I will try and help.

Answer 8

Sorry I don't follow that one. Suggest you repost it and let others see it.

Answer 9

Okay, thank you for taking a look though.

Answer 10

Angle DCO is 90 degrees because it is tangent.
\[\angle OCA + \angle DCO =\angle DCA = 144\]\[\angle ACO + 90 = 144\]\[\angle ACO = 54\]Triangle OAC is isoceles, therefore:\[\angle ACO = \angle CAO = 54\]\[\angle AOC + \angle ACO + \angle CAO = 180\]\[\angle AOC + 54 + 54 = 180\]\[\angle AOC = 180-108=72 = m \widehat{AC}\]\[m\widehat{CE}+m\widehat{EFA}+m\widehat{AC} =360\]\[m\widehat{CE}+214+72 =360\]