A) \[{{36}^{{}^\circ }},{{72}^{{}^\circ }},{{108}^{{}^\circ }},{{144}^{{}^\circ }}\]
B) \[{{45}^{{}^\circ }},{{110}^{{}^\circ }},{{55}^{{}^\circ }},{{150}^{{}^\circ }}\]
C) \[{{15}^{{}^\circ }},{{130}^{{}^\circ }},{{45}^{{}^\circ }},{{150}^{{}^\circ }}\]
D) none of these
Correct Answer: A
Solution :
(a): \[\angle are\text{ }6x,7x,8x,9x\] \[\Rightarrow 6x+7x+8x+9x=360{}^\circ -30x-{{360}^{{}^\circ }}.\] \[\therefore x={{12}^{{}^\circ }}\] \[\Rightarrow \angle are:{{72}^{{}^\circ }},{{84}^{{}^\circ }},{{96}^{{}^\circ }},{{108}^{{}^\circ }}\] Two \[\angle \] are OBTUSE Also, \[{{72}^{{}^\circ }}+{{108}^{{}^\circ }}={{180}^{{}^\circ }}and\,{{84}^{{}^\circ }}+{{96}^{{}^\circ }}={{180}^{{}^\circ }}\] \[\Rightarrow \]two pairs are supplementary
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