A) \[{{38}^{o}}\]
B) \[{{86}^{o}}\]
C) \[{{24}^{o}}\]
D) \[{{32}^{o}}\]
Correct Answer: A
Solution :
Given, \[\angle DAC={{32}^{o}}\]As \[DA||BC\]and AC is transversal. \[\therefore \]\[\angle ACB=\angle DAC={{32}^{o}}\] (alternate angles) Also, \[\angle AOB+\angle BOC={{180}^{o}}\](linear pair) \[\Rightarrow \]\[{{70}^{o}}+\angle BOC={{180}^{o}}\] \[\Rightarrow \]\[\angle BOC={{110}^{o}}\] In \[\Delta BOC,\angle BOC+\angle OBC+\angle OCB={{180}^{o}}\] (angle sum property) \[\Rightarrow \]\[{{110}^{o}}+\angle OBC+{{32}^{o}}={{180}^{o}}\] \[\Rightarrow \]\[\angle OBC={{180}^{o}}-({{110}^{o}}+{{32}^{o}})={{38}^{o}}\] \[\Rightarrow \]\[\angle DBC={{38}^{o}}\]You need to login to perform this action.
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