The measures of two angles of a cyclic quadrilateral are `40^(@)` and `110^(@)` Then, the measures of other two angles of the quadrilateral are ..........

Options

A. `400^(@) and 110^(@)`
B. `50^(@) and 100^(@)`
C. `140^(@) and 70^(@)`
D. `20 ^(@) and 120^(@)`

Answer

To find the measures of the other two angles of a cyclic quadrilateral when two angles are given, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Angles:**
We know two angles of the cyclic quadrilateral:
- Angle 1 = 40°
- Angle 2 = 110°

2. **Use the Property of Cyclic Quadrilaterals:**
In a cyclic quadrilateral, the sum of the opposite angles is equal to 180°.
- Therefore, we have:
- Angle 1 + Angle 3 = 180°
- Angle 2 + Angle 4 = 180°

3. **Calculate Angle 3:**
Using the property for Angle 1 and Angle 3:
- Angle 3 = 180° - Angle 1
- Angle 3 = 180° - 40°
- Angle 3 = 140°

4. **Calculate Angle 4:**
Using the property for Angle 2 and Angle 4:
- Angle 4 = 180° - Angle 2
- Angle 4 = 180° - 110°
- Angle 4 = 70°

5. **Conclusion:**
The measures of the other two angles of the cyclic quadrilateral are:
- Angle 3 = 140°
- Angle 4 = 70°

### Final Answer:
The measures of the other two angles of the quadrilateral are 140° and 70°.

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