Ash R.

asked • 09/15/14

in a trapezium ABCD, AB is parallel to DC, AB =AD, BD= DC and angle BAD = 128 degrees. find; angle ABD, angle BDC and angle BCD. (answer 26 deg, 26, 77)

geometry. i got ABD and BDC as 26 degrees. but, BCD is not 77 degrees, i m getting BCD as 128)

1 Expert Answer

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Phillip R. answered • 09/15/14

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triangle DAB is isosceles with AB = AD. One angle BAD is 128. Therefore the other two angles in the triangle are 26 degrees each. ABD = ADB = 26 degrees
 
BDC and ABD are alternate interior angles and therefore congruent.
 
BDC is also 26 degrees.
 
Triangle BCD is isosceles with BD=DC. One angle is 26. Therefore the other two angles in the triangle are 77 degrees each.
 
 
 
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Ash R.

sir as we knw that opposite angles are always equal. in trapezium ABCD, angle BAD and angles BCD are opposite. angle BCD must also be 128 degrees.
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09/17/14

Ash R.

let us suppose that opposite angle BCD is aldo 128 degrees. if we take angle BCD as 128 degrees then, angle BCD+ BDC + DBC (128 + 26 + 26 = 180 degrees) as we knw the sum of angles of a triangle is 180 degrees.
 
 
secondly i took DBC as 26 degrees because ADB and DBC are alternate interior angles.
 
 
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09/17/14

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