If ABCD is a cyclic quadrilateral with `angleA = 50^(@) , angleB = 80^(@)` , then `angleC` and `angleD` are

Options

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

Answer

To solve the problem of finding angles C and D in the cyclic quadrilateral ABCD, where angle A = 50° and angle B = 80°, we can follow these steps:

### Step 1: Understand the properties of cyclic quadrilaterals
In a cyclic quadrilateral, the sum of the opposite angles is equal to 180°. This means:
- Angle A + Angle C = 180°
- Angle B + Angle D = 180°

### Step 2: Use the given angle A to find angle C
We know that:
\[ \text{Angle A} + \text{Angle C} = 180° \]
Substituting the value of angle A:
\[ 50° + \text{Angle C} = 180° \]
To find angle C, we can rearrange the equation:
\[ \text{Angle C} = 180° - 50° \]
\[ \text{Angle C} = 130° \]

### Step 3: Use the given angle B to find angle D
Now, we can use angle B:
\[ \text{Angle B} + \text{Angle D} = 180° \]
Substituting the value of angle B:
\[ 80° + \text{Angle D} = 180° \]
To find angle D, we rearrange the equation:
\[ \text{Angle D} = 180° - 80° \]
\[ \text{Angle D} = 100° \]

### Conclusion
Thus, the values of angle C and angle D are:
- Angle C = 130°
- Angle D = 100°

### Final Answer
Angle C = 130°, Angle D = 100°.

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