If ABCD is a cyclic quadrilateral with `/_A = 50^@, /_B=80^@`, then `C and /_D` are

Options

A. `100^@, 130^@`
B. `115^@, 115^@`
C. `110^@, 120^@`
D. `130^@, 100^@`

Answer

To find the angles \( C \) and \( D \) in the cyclic quadrilateral \( ABCD \) where \( \angle A = 50^\circ \) and \( \angle B = 80^\circ \), we can use the properties of cyclic quadrilaterals.

### Step-by-Step Solution:

1. **Understand the Property of Cyclic Quadrilaterals**:
In a cyclic quadrilateral, the sum of the opposite angles is always \( 180^\circ \). This means:
\[ \angle A + \angle C = 180^\circ \]
\[ \angle B + \angle D = 180^\circ \]

2. **Calculate Angle \( C \)**:
We know \( \angle A = 50^\circ \). Using the property mentioned:
\[ \angle C = 180^\circ - \angle A \]
Substituting the value of \( \angle A \):
\[ \angle C = 180^\circ - 50^\circ = 130^\circ \]

3. **Calculate Angle \( D \)**:
We know \( \angle B = 80^\circ \). Using the property:
\[ \angle D = 180^\circ - \angle B \]
Substituting the value of \( \angle B \):
\[ \angle D = 180^\circ - 80^\circ = 100^\circ \]

4. **Final Result**:
Therefore, the angles are:
\[ \angle C = 130^\circ \quad \text{and} \quad \angle D = 100^\circ \]

### Summary:
- \( \angle C = 130^\circ \)
- \( \angle D = 100^\circ \)