In rhombus ABCD:
(i) if `angleA=74^(@)`, find `angleB and angleC`.
(ii) if `AD=7*5cm`, find BC and CD.

Answer

To solve the problem step by step, we will address each part of the question separately.

### Part (i): Finding angles B and C

1. **Identify the properties of a rhombus**: In a rhombus, opposite angles are equal, and the sum of all angles is 360 degrees.

2. **Given information**: We know that angle A = 74 degrees.

3. **Set up the equation for the angles**:
- Since angle A = angle C (opposite angles) and angle B = angle D (opposite angles), we can express the sum of the angles as:
\[ \text{angle A} + \text{angle B} + \text{angle C} + \text{angle D} = 360^\circ \]
- This can be rewritten using the known values:
\[ 74^\circ + \text{angle B} + 74^\circ + \text{angle B} = 360^\circ \]

4. **Combine like terms**:
- This simplifies to:
\[ 148^\circ + 2 \times \text{angle B} = 360^\circ \]

5. **Isolate angle B**:
- Subtract 148 degrees from both sides:
\[ 2 \times \text{angle B} = 360^\circ - 148^\circ \]
\[ 2 \times \text{angle B} = 212^\circ \]

6. **Divide by 2 to find angle B**:
- Therefore:
\[ \text{angle B} = \frac{212^\circ}{2} = 106^\circ \]

7. **Find angle C**: Since angle C = angle A, we have:
- \[ \text{angle C} = 74^\circ \]

### Summary of Part (i):
- Angle B = 106 degrees
- Angle C = 74 degrees

### Part (ii): Finding sides BC and CD

1. **Given information**: We know that AD = 7.5 cm.

2. **Properties of a rhombus**: All sides of a rhombus are equal, meaning:
- AB = BC = CD = AD

3. **Since AD = 7.5 cm**:
- Therefore, BC = 7.5 cm and CD = 7.5 cm.

### Summary of Part (ii):
- BC = 7.5 cm
- CD = 7.5 cm

### Final Answers:
- (i) Angle B = 106 degrees, Angle C = 74 degrees.
- (ii) BC = 7.5 cm, CD = 7.5 cm.