A) \[{{37}^{o}},\,\,{{143}^{o}},\,\,{{37}^{o}},\,\,{{143}^{o}}\]
B) \[{{108}^{o}},\,\,{{72}^{o}},\,\,{{108}^{o}},\,\,{{72}^{o}}\]
C) \[{{68}^{o}},\,\,{{112}^{o}},\,\,{{68}^{o}},\,\,{{112}^{o}}\]
D) None of these
Correct Answer: C
Solution :
Let the smallest angle be \[\angle A=x,\]and other adjacent angle\[\angle B={{(2x-24)}^{o}}\] Now, sum of adjacent angles of parallelogram is \[{{180}^{o}}.\] \[\therefore \]\[\angle A+\angle B={{180}^{o}}\] \[\Rightarrow \]\[x+2x-{{24}^{o}}={{180}^{o}}\] \[\Rightarrow \]\[3x={{204}^{o}}\Rightarrow x={{68}^{o}}\] \[\therefore \]\[A=x={{68}^{o}}\] and \[\angle B={{(2x-24)}^{o}}=2\times {{68}^{o}}-{{24}^{o}}={{112}^{o}}\] Since, opposite angles of a parallelogram are equal. So, \[\angle A=\angle C={{68}^{o}},\angle B=\angle D={{112}^{o}}\]You need to login to perform this action.
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