\[''\angle ABC={{30}^{\text{o}}},\,\angle EDF=(40-{{x}^{\text{o}}})\] and \[\angle ADE=13x+{{20}^{\text{o}}}''\].
A) \[\angle ABC=\angle EDF\]
B) \[\angle DBC\,+\angle EDF={{180}^{\text{o}}}\]
C) \[BC||DE\]
D) \[\angle BDE\] and \[\angle DBC\] are supplementary angles.
Correct Answer: D
Solution :
\[\angle ADE+\angle EDF={{180}^{\text{o}}}\] \[\Rightarrow \,\,40-x+13x+20={{180}^{\text{o}}}\] \[x=10\] \[\therefore \,\,\,\angle EDF={{30}^{\text{o}}}\,=\angle ABC\] A. is true. Also, \[BC||DE\,\,(\because \,\angle EDB=\angle DBC={{150}^{\text{o}}})\] \[\therefore \] C. is also true. Also, \[\angle DBC+\angle EDF={{150}^{\text{o}}}+{{30}^{\text{o}}}={{180}^{\text{o}}}\] \[\therefore \] B. is also true.
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