Question

In a triangle PQR, if ∠P + ∠R = 150° and ∠P + 3∠Q = 170°, then ∠P is:

• A. 70°
• B. 80°
• C. 75°
• D. 65°

Answer 1

The Correct Option is B

To solve the given problem, let's set up the equations based on the information: 

We are given:

• ∠P + ∠R = 150° (Equation 1)
• ∠P + 3∠Q = 170° (Equation 2)

We know the sum of angles in a triangle is 180°:

∠P + ∠Q + ∠R = 180° (Equation 3)

To find ∠P, we will:

1. Express ∠R from Equation 1:
2. Substitute ∠R in Equation 3:
3. Now use the value of ∠Q in Equation 2:

Thus, ∠P is 80°.

Answer 2

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.