ABCD is a rhombus . If angle ADB = 50 , find the angles of the rhombus ?

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Answer 1 · 2016-12-25T03:32:30

see explanation.

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Some of the properties of a rhombus are :

1) The sides of a rhombus are all congruent (the same length.)
#=> AB=BC=CD=DA#

2) #AC and BD# are perpendicular.

3) #AO=OC, and BO=OD#

4) #DeltaAOB, DeltaCOB, DeltaCOD and DeltaAOD# are congruent

.................

Now back to our question,

Given that #angleADB=50^@=angleADO#,

#angle OAD=90-50=40^@#

#=> angleOBA=angleOBC=angleODC=ODA=50^@#
#=> angleOAB=angleOCB=angleOCD=angleOAD=40^@#