Question

the side lengths of triangle abc are written in terms of the variable p, where p ≥ 3. which is correct regarding the angles of the triangle? a 4p - 1 p + 4 b c 3p m∠a > m∠c > m∠b m∠b > m∠a > m∠c m∠c > m∠a > m∠b m∠c > m∠b > m∠a

Explanation:

Step1: Identify sides opposite angles

• Side opposite ∠A: 3p
• Side opposite ∠B: p+4
• Side opposite ∠C: 4p-1

Step2: Compare side lengths (p≥3)

• 4p-1 vs 3p: 4p-1 - 3p = p-1 ≥2 >0 → 4p-1>3p
• 3p vs p+4: 3p - (p+4)=2p-4 ≥2>0 →3p>p+4
• Order: 4p-1>3p>p+4

Step3: Relate sides to angles

Larger side → larger opposite angle: ∠B>∠A>∠C

Answer:

B. m∠B > m∠A > m∠C