Question:
In a triangle PQR, if ∠P + ∠R = 150° and ∠P + 3∠Q = 170°, then ∠P is:
In a triangle PQR, if ∠P + ∠R = 150° and ∠P + 3∠Q = 170°, then ∠P is:
Updated On: Mar 28, 2025
- 70°
- 80°
- 75°
- 65°
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The Correct Option is B
Solution and Explanation
1. Triangle Angle Sum:
- In triangle PQR, we know that ∠P + ∠Q + ∠R = 180°.
2. Given Equations:
- ∠P + ∠R = 150° (Equation 1)
- ∠P + 3∠Q = 170° (Equation 2)
3. Substitute Equation 1 into the Triangle Angle Sum:
- From ∠P + ∠Q + ∠R = 180°, we can substitute ∠P + ∠R = 150°:
- 150° + ∠Q = 180°
- ∠Q = 180° - 150°
- ∠Q = 30°
4. Substitute ∠Q into Equation 2:
- Now, substitute ∠Q = 30° into ∠P + 3∠Q = 170°:
- ∠P + 3(30°) = 170°
- ∠P + 90° = 170°
- ∠P = 170° - 90°
- ∠P = 80°
Therefore, ∠P = 80°.
The correct answer is Option 2.
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