question_answer 1)

Find the value of the unknown exterior angle \[x\] in the following diagrams: (i)                 (ii)                      (iii) (iv)                     (v)                   (vi)                

Answer:

                \[x={{50}^{o}}+{{70}^{o}}\]         \[\left| \begin{align}   & \text{The exterior angle of a triangle i equal } \\  & \text{to the}~~\text{um of it two interior oppoite angle} \\ \end{align} \right.\] \[\Rightarrow \]               \[x={{120}^{o}}\] (ii)           \[x={{45}^{o}}+{{65}^{o}}\] \[\left| \begin{align}   & \text{The exterior angle of a triangle i equal} \\  & \text{to the um of it two interior angle} \\ \end{align} \right.\] \[\Rightarrow \]               \[x={{110}^{o}}\] (iii)          \[~x={{30}^{o}}+{{40}^{o}}\]               \[\left| \begin{align}   & \text{The exterior angle of a triangle i equal to} \\  & \text{the um of it two interior oppoite angle} \\ \end{align} \right.\] \[\Rightarrow \]               \[x={{70}^{o}}\] (iv)         \[x={{60}^{o}}+{{60}^{o}}\] \[\left| \begin{align}   & ~\text{The exterior angle of a triangle i equal to} \\  & \text{the um of it two interior oppoite angle} \\ \end{align} \right.\] \[\Rightarrow \]               \[x={{120}^{o}}\] (v)           \[x={{50}^{o}}+{{50}^{o}}\]               \[\left| \begin{align}   & \text{The exterior angle of a triangle i equal to} \\  & \text{the um of it two interior oppoite angle} \\ \end{align} \right.\] \[\Rightarrow \]               \[x={{100}^{o}}\]                 (vi)         \[x={{30}^{o}}+{{60}^{o}}\]                                         \[\left| \begin{align}   & \text{The exterior angle of a triangle i equal to} \\  & \text{the um of it two interior oppoite angle} \\ \end{align} \right.\] \[\Rightarrow \]               \[x={{90}^{o}}\]