ABCD is a cyclic quadrilateral. If `AD||BC and angle B = 70^(@),` find the other angles of ABCD.

Answer

To solve the problem, we need to find the angles of the cyclic quadrilateral ABCD given that AD is parallel to BC and angle B is 70 degrees.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- We know that ABCD is a cyclic quadrilateral.
- AD is parallel to BC.
- Angle B = 70 degrees.

2. **Use the Property of Cyclic Quadrilaterals:**
- In a cyclic quadrilateral, the sum of opposite angles is equal to 180 degrees.
- Therefore, we can write the equation for angles B and D:
\[ \text{Angle B} + \text{Angle D} = 180^\circ \]
- Substituting the value of angle B:
\[ 70^\circ + \text{Angle D} = 180^\circ \]

3. **Calculate Angle D:**
- Rearranging the equation gives us:
\[ \text{Angle D} = 180^\circ - 70^\circ = 110^\circ \]

4. **Use the Parallel Lines Property:**
- Since AD is parallel to BC, we can use the property of alternate interior angles.
- Therefore, we have:
\[ \text{Angle D} = \text{Angle A} + \text{Angle B} \]
- This means:
\[ 110^\circ = \text{Angle A} + 70^\circ \]

5. **Calculate Angle A:**
- Rearranging gives us:
\[ \text{Angle A} = 110^\circ - 70^\circ = 40^\circ \]

6. **Find Angle C Using Opposite Angles Property:**
- Again, using the property of cyclic quadrilaterals:
\[ \text{Angle A} + \text{Angle C} = 180^\circ \]
- Substituting the value of angle A:
\[ 40^\circ + \text{Angle C} = 180^\circ \]

7. **Calculate Angle C:**
- Rearranging gives us:
\[ \text{Angle C} = 180^\circ - 40^\circ = 140^\circ \]

### Summary of Angles:
- Angle A = 110 degrees
- Angle B = 70 degrees
- Angle C = 140 degrees
- Angle D = 110 degrees

### Final Answer:
- Angle A = 110°
- Angle B = 70°
- Angle C = 140°
- Angle D = 110°