ABCD is a cyclic quadrilateral. AB and DC are produced to meet at P. If `angleADC = 70degree and angleDAB = 60degree`, then the `anglePBC + anglePCB` is

Options

A. `130^@`
B. `150^@`
C. `155^@`
D. `180^@`

Answer

To solve the problem, we will use the properties of cyclic quadrilaterals and the angles formed by the intersection of lines.

### Step-by-Step Solution:

1. **Understanding the Cyclic Quadrilateral**:
- A cyclic quadrilateral is a quadrilateral whose vertices lie on a circle. The opposite angles of a cyclic quadrilateral are supplementary.

2. **Given Angles**:
- We are given that \( \angle ADC = 70^\circ \) and \( \angle DAB = 60^\circ \).

3. **Finding Angle ABC**:
- In a cyclic quadrilateral, the angle opposite to \( \angle ADC \) is \( \angle ABC \).
- Therefore, \( \angle ABC = 180^\circ - \angle ADC = 180^\circ - 70^\circ = 110^\circ \).

4. **Finding Angle DAB**:
- We already have \( \angle DAB = 60^\circ \).

5. **Finding Angles PBC and PCB**:
- The angles \( \angle PBC \) and \( \angle PCB \) are the angles formed at point P by the lines AB and DC.
- By the exterior angle theorem, we know that:
\[ \angle PBC + \angle PCB = \angle DAB + \angle ADC \]
- Substitute the values:
\[ \angle PBC + \angle PCB = 60^\circ + 70^\circ = 130^\circ \]

6. **Final Answer**:
- Therefore, \( \angle PBC + \angle PCB = 130^\circ \).

### Conclusion:
The value of \( \angle PBC + \angle PCB \) is \( 130^\circ \).