• # question_answer If the angles of a quadrilateral are in A.P. whose common difference is${{10}^{o}}$, then the angles of the quadrilateral are A) ${{65}^{o}},\,{{85}^{o}},\,{{95}^{o}},\,{{105}^{o}}$ B) ${{75}^{o}},\,{{85}^{o}},\,{{95}^{o}},\,{{105}^{o}}$ C) ${{65}^{o}},\,{{75}^{o}},\,{{85}^{o}},\,{{95}^{o}}$ D) ${{65}^{o}},\,{{95}^{o}},\,{{105}^{o}},\,{{115}^{o}}$

Suppose that$\angle A={{x}^{0}}$, then$\angle B=x+{{10}^{o}}$, $\angle C=x+{{20}^{o}}$and$\angle D=x+{{30}^{o}}$ So, we know that $\angle A+\angle B+\angle C+\angle D=2\pi$ Putting these values, we get $({{x}^{o}})+({{x}^{o}}+{{10}^{o}})+({{x}^{o}}+{{20}^{o}})+({{x}^{o}}+{{30}^{o}})={{360}^{o}}$ $\Rightarrow x={{75}^{o}}$ Hence the angles of the quadrilateral are${{75}^{o}},\ {{85}^{o}},\ {{95}^{o}},\ {{105}^{o}}$. Trick: In these type of questions, students should satisfy the conditions through options. Here B satisfies both the conditions $i.e.$ angles are in A.P. with common difference ${{10}^{o}}$and sum of angles is${{360}^{o}}$.