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

The problem is solved by establishing equations from the provided data:

Given:

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

The sum of angles in a triangle is 180°:

∠P + ∠Q + ∠R = 180° (Equation 3)

To determine ∠P, the following steps are performed:

1. Isolate ∠R using Equation 1.
2. Substitute the expression for ∠R into Equation 3.
3. Utilize the derived value of ∠Q in Equation 2.

Consequently, ∠P equals 80°.