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Question

Question 164
Two angles of a quadrilateral are each of measure 75 and the other two angles are equal. What is the measure of these two angles? Name the possible figures so formed.

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Solution

Let ABCD be a quadrilateral,
where A=C=75 and B=D=x [say]

Then, by the angle sum property of a quadrilateral, we have
A+B+C+D=36075+x+75+x=3602x=3601502x=210x=105
Thus, other two angles are of 105 each.
Since, opposite angles are equal, therefore the quadrilateral is a parallelogram.

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