Find angles x and y, as show in the figure.

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Solution

Opposite angles are equal,
so, $L A B C = 60 ° \Rightarrow x = 60 °$
Using the sum of angles of a triangle is $180 ° i n △ A B C, L A B C + L B C A + L C A B = 180 ° \Rightarrow 60 ° + y + 30 ° = 180 ° \Rightarrow y + 90 ° = 180 ° \Rightarrow y = 90 °$

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