The ratio of the angle `angleA" and "angle B` of a non-square rhombus ABCD is 4 : 5, then the value of `angleC` is :

Options

A. `50^(@)`
B. `45^(@)`
C. `80^(@)`
D. `95^(@)`

Answer

To solve the problem, we need to find the value of angle C in a rhombus ABCD where the ratio of angle A to angle B is given as 4:5.

### Step-by-Step Solution:

1. **Understand the Properties of a Rhombus**:
In a rhombus, opposite angles are equal, and adjacent angles are supplementary (i.e., they add up to 180 degrees).

2. **Set Up the Ratio**:
Let angle A = 4x and angle B = 5x, where x is a common multiplier.

3. **Use the Supplementary Angle Property**:
Since angle A and angle B are adjacent angles, we can write the equation:
\[ \text{Angle A} + \text{Angle B} = 180^\circ \]
Substituting the values we have:
\[ 4x + 5x = 180^\circ \]

4. **Combine Like Terms**:
\[ 9x = 180^\circ \]

5. **Solve for x**:
\[ x = \frac{180^\circ}{9} = 20^\circ \]

6. **Find the Angles A and B**:
Now substitute x back into the expressions for angle A and angle B:
\[ \text{Angle A} = 4x = 4 \times 20^\circ = 80^\circ \]
\[ \text{Angle B} = 5x = 5 \times 20^\circ = 100^\circ \]

7. **Find Angle C**:
Since angle C is opposite to angle A, we have:
\[ \text{Angle C} = \text{Angle A} = 80^\circ \]

### Final Answer:
The value of angle C is \( 80^\circ \).

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