State 'T' for true and 'F' for false and select the correct option.
(i) The measure of each exterior angle of an n-sided regular polygon is `((180^(@))/(n))`.
(ii) The adjacent angles in a parallelogram are supplementary.
(iii) In a quadrilateral PQRS, the bisector of `angleP and angleQ` meet at point M. If `angleR = 120^(@) and angleS = 40^(@)`, then `anglePMQ = 80^(@)`

Options

A. `{:(i,ii,iii),(F,F,T):}`
B. `{:(i,ii,iii),(F,T,T):}`
C. `{:(i,ii,iii),(T,F,F):}`
D. `{:(i,ii,iii),(T,T,F):}`

Answer

Let's solve the question step by step.

### Step 1: Evaluate Statement (i)
**Statement:** The measure of each exterior angle of an n-sided regular polygon is \(\frac{180^\circ}{n}\).

**Solution:**
- The formula for the measure of each exterior angle of a regular polygon is actually \(\frac{360^\circ}{n}\), not \(\frac{180^\circ}{n}\).
- Therefore, this statement is **False (F)**.

### Step 2: Evaluate Statement (ii)
**Statement:** The adjacent angles in a parallelogram are supplementary.

**Solution:**
- In a parallelogram, adjacent angles are indeed supplementary, meaning their sum is \(180^\circ\).
- This is a property of parallelograms, so this statement is **True (T)**.

### Step 3: Evaluate Statement (iii)
**Statement:** In a quadrilateral PQRS, the bisector of angle P and angle Q meet at point M. If \(\angle R = 120^\circ\) and \(\angle S = 40^\circ\), then \(\angle PMQ = 80^\circ\).

**Solution:**
1. Let \(\angle P = 2x\) and \(\angle Q = 2y\) (since they are bisected).
2. The sum of the angles in a quadrilateral is \(360^\circ\):
\[ 2x + 2y + \angle R + \angle S = 360^\circ \]
Substituting the known angles:
\[ 2x + 2y + 120^\circ + 40^\circ = 360^\circ \]
Simplifying gives:
\[ 2x + 2y + 160^\circ = 360^\circ \]
\[ 2x + 2y = 200^\circ \]
\[ x + y = 100^\circ \]

3. In triangle PMQ, the sum of the angles is \(180^\circ\):
\[ x + y + \angle PMQ = 180^\circ \]
Substituting \(x + y = 100^\circ\):
\[ 100^\circ + \angle PMQ = 180^\circ \]
Therefore:
\[ \angle PMQ = 180^\circ - 100^\circ = 80^\circ \]
This statement is **True (T)**.

### Final Evaluation:
- (i) **False (F)**
- (ii) **True (T)**
- (iii) **True (T)**

### Correct Option:
The correct option is the one that states (i) is False, (ii) is True, and (iii) is True.

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