In a rhombus ABCD, `/_`ABC = `72^(@)`. Find `/_`ACD

Answer

To find the angle ACD in rhombus ABCD where angle ABC is given as 72°, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Properties of a Rhombus**:
In a rhombus, opposite angles are equal, and adjacent angles are supplementary (they add up to 180°).

2. **Identify Given Information**:
We know that angle ABC = 72°.

3. **Determine Angle ADC**:
Since opposite angles in a rhombus are equal, angle ADC is also 72°.

\[ \text{Angle ADC} = \text{Angle ABC} = 72° \]

4. **Set Up the Triangle**:
Consider triangle ACD. In this triangle, we know:
- Angle ADC = 72°
- Angles DAC and ACD are equal because AD = DC (sides of the rhombus).

Let’s denote angle DAC = angle ACD = y.

5. **Use the Triangle Sum Property**:
The sum of angles in triangle ACD is 180°. Therefore, we can write the equation:

\[ \text{Angle ADC} + \text{Angle DAC} + \text{Angle ACD} = 180° \]

Substituting the known values:

\[ 72° + y + y = 180° \]

This simplifies to:

\[ 72° + 2y = 180° \]

6. **Solve for y**:
To isolate y, first subtract 72° from both sides:

\[ 2y = 180° - 72° \]

\[ 2y = 108° \]

Now, divide both sides by 2:

\[ y = \frac{108°}{2} = 54° \]

7. **Conclusion**:
Therefore, angle ACD is:

\[ \text{Angle ACD} = 54° \]

### Final Answer:
Angle ACD = 54°.