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O is the centre of the circle. we know that the if an arc subtends angle "X" at the circumference then it subtends an angle of "2X" at the centre. hence looking at the fig. we can say that arc AB subtends angle "t" at the circumference and angle "x" at the centre. therefore x=2t. similarly y=2z. hence (x + y) = 2*(z + t).
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