In a parallelogram `PQRS`, angle P is four times of angle Q, then the measure of `/_R` is

Options

A. `144^@`
B. `36^@`
C. `72^@`
D. `130^@`

Answer

To solve the problem, we need to use the properties of a parallelogram and the relationship between its angles.

### Step-by-Step Solution:

1. **Understand the properties of a parallelogram**: In a parallelogram, opposite angles are equal, and the sum of adjacent angles is 180 degrees.

2. **Define the angles**: Let angle Q be represented as \( x \). According to the problem, angle P is four times angle Q. Therefore, we can express angle P as:
\[ \text{Angle P} = 4x \]

3. **Use the property of adjacent angles**: Since angles P and Q are adjacent angles in the parallelogram, we can write the equation based on the property that their sum equals 180 degrees:
\[ \text{Angle P} + \text{Angle Q} = 180^\circ \]
Substituting the expressions for angles P and Q, we have:
\[ 4x + x = 180^\circ \]

4. **Combine like terms**: Simplifying the equation gives:
\[ 5x = 180^\circ \]

5. **Solve for x**: To find the value of \( x \), divide both sides by 5:
\[ x = \frac{180^\circ}{5} = 36^\circ \]

6. **Find angle P**: Now that we have the value of \( x \), we can find angle P:
\[ \text{Angle P} = 4x = 4 \times 36^\circ = 144^\circ \]

7. **Determine angle R**: Since angle R is opposite angle P in the parallelogram, it is equal to angle P:
\[ \text{Angle R} = \text{Angle P} = 144^\circ \]

### Final Answer:
The measure of angle R is \( 144^\circ \).