Two adjacent angles of a quadrilateral ABCD (having two pairs of parallel opposite sides with adjacent side of unequal length) measure (6x+30)° and (110-2x)°. prove that ABCD is rectangle.
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Answer:
(6x+30)°+(110-2x)° = 180 (Co-interior angles property)
6x+30+110-2x = 180
4x+140 = 180
4x = 180-140
4x = 40
x = 10
Now,
6x+30 = 6×10+30
= 90°
110-2x = 110-2×10
= 110-20
= 90°
Since, two angles of the quadrilateral are 90, their adjacent angles will be 90 too. This proves that the quadrilateral is a rectangle.
hope this helps <3
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