Question

$\text{Construct a triangle whose perimeters 10.4 cm and the base angles are}{45}^{\circ }and{120}^{\circ }$

Answer 1

Steps of construction:
1. Draw a line segment PQ = 10.4 cm.
2. Construct an angle of 45° and bisect it to get $\angle QPX$.
3. Construct an angle of 120° and bisect it to get $\angle PQY$.
4. The ray XP and YQ intersect at A.
5. Draw the right bisectors of AP and AQ, cutting PQ at B and C, respectively.
6. Join AB and AC.
Thus, △ ABC is the required triangle.