PQRS is a trapezium in which PQ||SR and `angleP=130°`, `angleQ=110°`. Then `angleR` is equal to:

Options

A. 70°
B. 50°
C. 65°
D. 55°

Answer

To find the value of angle R in trapezium PQRS where PQ is parallel to SR, and given that angle P = 130° and angle Q = 110°, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Properties of a Trapezium**:
In a trapezium, the sum of the angles on the same side of the transversal (the line connecting the parallel sides) is equal to 180°. This means that angle P and angle R are supplementary, as well as angle Q and angle S.

2. **Identify the Given Angles**:
We know:
- Angle P = 130°
- Angle Q = 110°

3. **Using the Supplementary Angle Property**:
Since angle P and angle R are on the same side of the transversal, we can write the equation:
\[ \text{Angle P} + \text{Angle R} = 180° \]
Substituting the value of angle P:
\[ 130° + \text{Angle R} = 180° \]

4. **Solving for Angle R**:
To find angle R, we can rearrange the equation:
\[ \text{Angle R} = 180° - 130° \]
\[ \text{Angle R} = 50° \]

5. **Conclusion**:
Therefore, the value of angle R is 50°.

### Final Answer:
Angle R = 50°

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