[Enrique]

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Angle green = angle pink since it is subtended by the same chord . (ie , the chord formed from the vertices of the green angle and yellow angle )


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Green and pink are not necessarily equal.

Z

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I think it's clear when I say that the angles are equal because it is subtended by the same chord . It is very easy to show that blue = yellow + red since the sum of the angles of a triangle is 180 .

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You wrote angle green = angle pink.
That statement is false. Although you give the explanation about angle green and angle yellow opening the same chord, hence angle green = angle yellow. And now you can say angle blue = angle yellow + angle red