A) \[a={{114}^{{}^\circ }},b={{46}^{{}^\circ }},c={{114}^{{}^\circ }}\]
B) \[a={{104}^{{}^\circ }},b={{56}^{{}^\circ }},c={{114}^{{}^\circ }}\]
C) \[a={{114}^{{}^\circ }},b={{26}^{{}^\circ }},c={{154}^{{}^\circ }}\]
D) \[a={{94}^{{}^\circ }},b={{46}^{{}^\circ }},c={{54}^{{}^\circ }}\]
Correct Answer: A
Solution :
(a): \[\therefore \] \[AB\parallel CD\] and GH is transversal \[\therefore \]\[g={{66}^{{}^\circ }}=d\] Also, \[g+c={{180}^{{}^\circ }}\] [Linear pair] \[c=180-66={{114}^{{}^\circ }}\] \[\therefore \]\[EF\parallel GH\] \[\therefore \] \[a=c={{114}^{{}^\circ }}\] Now, \[a+d+134+i={{360}^{{}^\circ }}\] \[\therefore \]\[{{114}^{{}^\circ }}+{{66}^{{}^\circ }}+{{134}^{{}^\circ }}+i={{360}^{{}^\circ }}\] \[i={{360}^{{}^\circ }}-{{314}^{{}^\circ }}={{46}^{{}^\circ }}\] \[\therefore \]\[b=i={{46}^{{}^\circ }}\]
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