The flowers of dicotyledons are typically trimerous while monocots possess pentamerous flowers.

Answer

To determine whether the statement "The flowers of dicotyledons are typically trimerous while monocots possess pentamerous flowers" is true or false, we can break down the terms and characteristics of dicotyledons and monocots.

### Step-by-Step Solution:

1. **Understanding Flower Structure**:
- **Trimerous Flowers**: These flowers have parts that are in multiples of three. This means that the petals, sepals, and stamens typically come in groups of three.
- **Pentamerous Flowers**: These flowers have parts that are in multiples of five. This means that the petals, sepals, and stamens typically come in groups of five.

2. **Identifying Flower Types**:
- **Dicotyledons (Dicots)**: These plants usually have flowers that are pentamerous. This means that their floral parts (petals, sepals, stamens) are often in groups of five or multiples of five.
- **Monocotyledons (Monocots)**: These plants typically have trimerous flowers, meaning their floral parts are usually in groups of three.

3. **Evaluating the Statement**:
- The statement claims that dicots are trimerous and monocots are pentamerous. However, based on the definitions:
- Dicots are generally pentamerous.
- Monocots are generally trimerous.
- Therefore, the statement is incorrect.

4. **Conclusion**:
- The statement "The flowers of dicotyledons are typically trimerous while monocots possess pentamerous flowers" is **false**.

### Final Answer:
The statement is **false**.