In a parallelogram PQRS, if `angleP = 60°`, then other three angles are

Options

A. 45°, 135°, 120°
B. 60°, 120°, 120°
C. 60°, 135°, 135°
D. 45°, 135°, 135°

Answer

To find the other three angles in the parallelogram PQRS, given that angle P = 60°, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Angle**: We know that angle P = 60°.

2. **Use the Property of Parallelograms**: In a parallelogram, adjacent angles are supplementary. This means that the sum of angle P and angle Q is 180°.
\[ \text{Angle P} + \text{Angle Q} = 180° \]

3. **Calculate Angle Q**: Since angle P = 60°, we can find angle Q as follows:
\[ 60° + \text{Angle Q} = 180° \]
\[ \text{Angle Q} = 180° - 60° = 120° \]

4. **Use the Property of Opposite Angles**: In a parallelogram, opposite angles are equal. Therefore:
\[ \text{Angle R} = \text{Angle P} = 60° \]
\[ \text{Angle S} = \text{Angle Q} = 120° \]

5. **Summarize the Angles**: Now we can summarize the angles in parallelogram PQRS:
- Angle P = 60°
- Angle Q = 120°
- Angle R = 60°
- Angle S = 120°

### Final Answer:
The angles in parallelogram PQRS are:
- Angle P = 60°
- Angle Q = 120°
- Angle R = 60°
- Angle S = 120°