In `∆PQR`, if `∠ P = 60°, and ∠ Q = 40°`, then the exterior angle formed by producing QR is equal to

Options

A. `60^@`
B. `120^@`
C. `100^@`
D. `80^@`

Answer

To solve the problem, we need to find the exterior angle formed by producing side QR in triangle PQR, given that ∠P = 60° and ∠Q = 40°.

### Step-by-Step Solution:

1. **Identify the Angles in Triangle PQR**:
- We are given that ∠P = 60° and ∠Q = 40°.

2. **Calculate the Third Angle (∠R)**:
- The sum of the angles in a triangle is always 180°.
- Therefore, we can find ∠R using the formula:
\[ ∠R = 180° - (∠P + ∠Q) \]
- Substituting the known values:
\[ ∠R = 180° - (60° + 40°) = 180° - 100° = 80° \]

3. **Understanding the Exterior Angle**:
- The exterior angle formed by extending side QR (let's call it ∠PRX) is equal to the sum of the two opposite interior angles (∠P and ∠R).
- According to the exterior angle theorem:
\[ ∠PRX = ∠P + ∠R \]

4. **Calculate the Exterior Angle (∠PRX)**:
- Now, substitute the values of ∠P and ∠R:
\[ ∠PRX = ∠P + ∠R = 60° + 80° = 140° \]

5. **Conclusion**:
- Therefore, the exterior angle formed by producing QR is 140°.

### Final Answer:
The exterior angle formed by producing QR is **140°**.