question_answer 13)

Examine whether you can construct \[\Delta \text{DEF}\] such that \[\text{EF}=\text{7}.\text{2 cm},\text{ m }\angle E=\text{11}{{0}^{\text{o}}}\] and \[m\angle F={{80}^{\text{o}}}\]. Justify your answer.

Answer:

                \[m\angle E+m\angle F={{110}^{\text{o}}}+{{80}^{\text{o}}}={{190}^{\text{o}}}>{{180}^{\text{o}}}\] This is not possible since the sum of the measures of the three angles of a triangle is \[\text{18}{{0}^{\text{o}}}\]. As such, the sum of two angles of a triangle cannot exceed\[\text{18}{{0}^{\text{o}}}\]. Hence, \[\Delta \text{DEF}\] cannot be constructed.