Question

ABCD is a rhombus. If angle DAC= 50°, find (a) angle ADC (b) angle
CAB, including picture​

Answer 1

Step-by-step explanation:

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) ACandBD are perpendicular.

3) AO=OC,andBO=OD

4) ΔAOB, ΔCOB ,ΔCODandΔAOD

are congruent

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

Now back to our question,

Given that ∠ADB=50∘=∠ADO ,

∠OAD=90−50=40∘

⇒∠OBA=∠OBC=∠ODC=ODA=50∘

⇒∠OAB=∠OCB=∠OCD= ∠OAD=40∘

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