Calculating the measurement of the arc of a circle with a triangle inside

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Hello,

I've been trying to understand the solution to the problem above. I am confused as to how the solution can declare that angle DQE = (arc BC + arc DE)/2 and angle CPQ = (arc CD - arc BC)/2. I'd really appreciate an explanation.

Thanks ^_^

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See this article. That's a generalization of Thales Theorem known as the inscribed angle theorem.