Question:
Construct a triangle whose perimeter is 10.4 cm and the base angles are 45° and 120°.
Solution:
Steps of construction:
1. Draw a line segment PQ = 10.4 cm.
2. Construct an angle of $45^{\circ}$ and bisect it to get $\angle Q P X$.
3. Construct an angle of $120^{\circ}$ and bisect it to get $\angle P Q Y$.
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, $\triangle A B C$ is the required triangle.