Calculate the angles in the triangle

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To calculate the angles in a triangle, remember that all angles must sum to 180 degrees. In a right triangle, one angle is 90 degrees, while an isosceles triangle has two equal angles. The central angle is twice the inscribed angle subtended by the same arc, which helps in determining angles in the triangle. Drawing lines from the center of the circle to the triangle's vertices creates isosceles triangles, aiding in angle calculations. Understanding these geometric principles simplifies the problem significantly.
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Need some help with this one. Please be detailed and methodic in your understandable explanations because I find this very difficult.

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basically all the angles in a triangle have to add up to 180' degrees, depending on the triangle formation you can tell what one of the angles could be - i.e a right angle triange will have a 90' degree angle and a icosilees (cant spell) triangle will have two angles the same and one different, an equilateral triangle all angles the same.
 
I will give you a couple of hints to get you going. Call the center of the circle O and draw lines from O to A, B, and C. These lines will make three isosceles triangles with the sides of the given triangle. The theorem from geometry you need to remember is that the central angle is twice the size of an inscribed angle subtended by the same arc. For example, in this problem, angle AOC is twice angle you have labeled 80 degrees. So you should be able to figure out the central angles in that triangle and use the isosceles triangles to get the others. Good luck.
 
LCKurtz said:
I will give you a couple of hints to get you going. Call the center of the circle O and draw lines from O to A, B, and C. These lines will make three isosceles triangles with the sides of the given triangle. The theorem from geometry you need to remember is that the central angle is twice the size of an inscribed angle subtended by the same arc. For example, in this problem, angle AOC is twice angle you have labeled 80 degrees. So you should be able to figure out the central angles in that triangle and use the isosceles triangles to get the others. Good luck.

Ok thanks. But there must be a easier way to look at the problem
 
I don't think so. This is pretty easy. Did you try it?
 
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