question_answer 7)

                (a) Find \[x+y+z\]                 (b) Find \[x+y+z+\omega \]

Answer:

                (a) By linear pair property and angle sum property of a triangle, \[({{180}^{\text{o}}}-x)+({{180}^{\text{o}}}-z)\,+({{180}^{\text{o}}}-y)\] \[={{180}^{o}}\] \[\Rightarrow \]               \[x+y+z={{360}^{\text{o}}}\]. (b) By linear pair property and angle sum property of a quadrilateral,           \[({{180}^{o}}-x)+({{180}^{o}}-y)+({{180}^{o}}-z)\]\[+({{180}^{o}}-w)={{360}^{o}}\] \[\Rightarrow \]               \[x+y+z+w={{360}^{\text{o}}}\].