Question

1. if ( mangle lmp ) is 11 degrees more than ( mangle nmp ) and ( mangle nml = 137^{circ} ), find each measure.

( mangle lmp=)
( mangle nmp=)

Explanation:

Step1: Set up the equation

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

Step2: Simplify the equation

Combine like - terms: \(2x+11 = 137\).
Subtract 11 from both sides: \(2x=137 - 11\), so \(2x=126\).

Step3: Solve for \(x\)

Divide both sides by 2: \(x=\frac{126}{2}=63\).

Answer:

\(m\angle NMP = 63^{\circ}\), \(m\angle LMP=74^{\circ}\)