Question

if m∠lmp is 11 degrees more than m∠nmp and m∠nml = 137°, find m∠nmp

Explanation:

Step1: Set up an equation

Let \(m\angle NMP = x\). Then \(m\angle LMP=x + 11\). Since \(m\angle NML=m\angle NMP + m\angle LMP\) and \(m\angle NML = 137^{\circ}\), we have the equation \(x+(x + 11)=137\).

Step2: Simplify the equation

Combine like - terms: \(2x+11 = 137\).

Step3: Solve for \(x\)

Subtract 11 from both sides: \(2x=137 - 11=126\). Then divide both sides by 2: \(x=\frac{126}{2}=63\).

Answer:

\(63^{\circ}\)