Question

Construct a triangle whose perimeter is $10.4cm$ and whose base angles are ${45}^{\circ }$ and ${120}^{\circ }$.

Answer 1

Steps of construction:
1. Draw a line segment XY = 10.4 cm.
2. Make angle ∠LXY = ∠B = 45° and ∠MYX = ∠C = 120°.
3. Bisect ∠LXY and ∠MYX. Let these bisectors intersect at a point A (say).
4. Draw perpendicular bisectors PQ and RS of AX and AY, respectively.
5. Let PQ intersect XY at B and RS intersect XY at C.
6. Join AB and AC.

Then, △ ABC is the required triangle.