question_answer 8)

                Find \[x\] in the following figures.                 (a) (b)

Answer:

                (a) \[{{x}^{\text{o}}}+{{125}^{\text{o}}}+{{125}^{\text{o}}}={{360}^{\text{o}}}\]. | \[\because \] The sum of the measures of the exterior angles of any polygon is \[{{360}^{o}}\] \[\Rightarrow \]               \[x+{{250}^{\text{o}}}={{360}^{\text{o}}}\] \[\Rightarrow \]               \[x={{360}^{\text{o}}}-{{250}^{\text{o}}}\] \[\Rightarrow \]               \[x={{110}^{\text{o}}}\]                 (b) \[x+{{70}^{\text{o}}}+{{60}^{\text{o}}}+({{90}^{\text{o}}}+{{90}^{\text{o}}})={{360}^{\text{o}}}\]. | \[\because \] The sum of the measures of the exterior angles of any polygon is\[{{360}^{o}}\]. \[\Rightarrow \]               \[x+{{310}^{\text{o}}}={{360}^{\text{o}}}\] \[\Rightarrow \]               \[x={{360}^{\text{o}}}-{{310}^{\text{o}}}\] \[\Rightarrow \]               \[x={{50}^{\text{o}}}\].