Question

Construct a triangle 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. 

∠F + ∠E + ∠G = 180°

⇒ 65° + ∠E + 45° = 180°

⇒ ∠E = 70°

Steps of construction:

1. Draw a line EG = 6 cm.
2. With E as a centre, draw ∠XEG = 70°.
3. With G as a centre, draw ∠YGE = 45º.
4. Let YG and XE meet at point F. 

∆FEG is the required triangle.