In cyclic quadrilateral `PQRS`, `/_SQR = 60^(@)` and `/_QPR = 20^(@)`. Then, `/_QRS=`

Options

A. `40^(@)`
B. `60^(@)`
C. `80^(@)`
D. `100^(@)`

Answer

To find the angle \( \angle QRS \) in the cyclic quadrilateral \( PQRS \), we can follow these steps:

### Step 1: Identify the given angles
We are given:
- \( \angle SQR = 60^\circ \)
- \( \angle QPR = 20^\circ \)

### Step 2: Use the property of cyclic quadrilaterals
In cyclic quadrilaterals, the angles subtended by the same arc are equal. Therefore, we can say:
\[ \angle QPR = \angle QSR \]
This means:
\[ \angle QSR = 20^\circ \]

### Step 3: Apply the triangle angle sum property
Now, we will consider triangle \( QSR \). The sum of the angles in a triangle is always \( 180^\circ \). Therefore, we can write:
\[ \angle QSR + \angle SQR + \angle QRS = 180^\circ \]
Substituting the known values:
\[ 20^\circ + 60^\circ + \angle QRS = 180^\circ \]

### Step 4: Solve for \( \angle QRS \)
Now, we can solve for \( \angle QRS \):
\[ \angle QRS = 180^\circ - (20^\circ + 60^\circ) \]
\[ \angle QRS = 180^\circ - 80^\circ \]
\[ \angle QRS = 100^\circ \]

### Conclusion
Thus, the measure of \( \angle QRS \) is \( 100^\circ \).

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