A) \[100{}^\circ \], \[160{}^\circ \]
B) \[\text{110 }\!\!{}^\circ\!\!\text{ }\], \[150{}^\circ \]
C) \[120{}^\circ \], \[140{}^\circ \]
D) \[\text{110 }\!\!{}^\circ\!\!\text{ }\], \[130{}^\circ \]
Correct Answer: C
Solution :
In\[\Delta OCD\], We have \[\angle DOC+\angle ODC+\angle DCO=180{}^\circ \] [Angle sum property] \[\Rightarrow \angle DOC+30{}^\circ +30{}^\circ =180{}^\circ \] \[\angle DOC=180{}^\circ -60{}^\circ =120{}^\circ \] Now, in quadrilateral ABCD, we have \[\angle DAB+\angle ADC+\angle BCD+\angle ABC=360{}^\circ \] \[\Rightarrow 100{}^\circ +60{}^\circ +60{}^\circ +\angle ABC=360{}^\circ \] \[\Rightarrow 220{}^\circ +\angle ABC=360{}^\circ \] \[\Rightarrow \angle ABC=360{}^\circ -220{}^\circ =140{}^\circ \]You need to login to perform this action.
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