Question

Construct triangles of the measures given below.
In ∆EFG, l(EG) = 6 cm, m∠F = 65^°, m∠G = 45^°

Answer 1

Using the angle sum property, we can find the third angle of the triangle FEG.
$$\begin{gathered} \angle \mathrm{F}+\angle \mathrm{E}+\angle \mathrm{G}=180° \\ \Rightarrow 65°+\angle \mathrm{E}+45°=180° \\ \Rightarrow \angle \mathrm{E}=70° \end{gathered}$$
Steps of construction:
1. Draw a line EG = 6 cm.
2. With E as centre, draw ∠XEG = 70$°$.
3. With G as centre, draw ∠YGE = 45º.
4. Let YG and XE meet at point F.
∆FEG is the required triangle.