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Question -

The opposite sides of a quadrilateral are parallel. If one angle of the quadrilateral is 60┬░, find the other angles.



Answer -

In quadrilateral ABCD, AB || DC and AD || BC and тИаA = 60┬░
┬а
тИ╡ AD || BC and AB || DC
тИ┤ ABCD is a parallelogram
тИ┤ тИаA + тИаB = 180┬░ (Co-interior angles)
60┬░ + тИаB = 180┬░
тЗТ тИаB = 180┬░-60┬░= 120┬░
But тИаA = тИаC and тИаB = тИаD (Opposite angles of a ||gm)
тИ┤ тИаC = 60┬░ and тИаD = 120┬░
Hence тИаB = 120┬░, тИаC = 60┬░ and тИаD = 120┬░

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