A) \[{{64}^{{}^\circ }}\]
B) \[{{84}^{{}^\circ }}\]
C) \[{{56}^{{}^\circ }}\]
D) \[{{96}^{{}^\circ }}\]
Correct Answer: C
Solution :
(c): Let \[\angle ACD=a=\angle DAC\] \[\therefore \] \[\angle CDB=2a=\angle CBD\] The angles of the base of an isosceles triangle are equal. \[\therefore \] \[\angle ACB={{180}^{{}^\circ }}-{{84}^{{}^\circ }}={{96}^{{}^\circ }}\] \[\Rightarrow \]\[\angle ACD+\angle DCB={{96}^{{}^\circ }}\] \[\Rightarrow \]\[a+{{180}^{{}^\circ }}-4a={{96}^{{}^\circ }}\] \[\Rightarrow \]\[{{180}^{{}^\circ }}-3a={{96}^{{}^\circ }}\] \[\Rightarrow \]\[3a={{180}^{{}^\circ }}-{{96}^{{}^\circ }}={{84}^{{}^\circ }}\] \[\Rightarrow \] \[a=\frac{{{84}^{{}^\circ }}}{3}={{28}^{{}^\circ }}\] \[\Rightarrow \]\[\angle DBC=2a={{56}^{{}^\circ }}\]You need to login to perform this action.
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