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 variables

Let $m\angle NMP = x$. Then $m\angle LMP=x + 11$.

Step2: Use angle - sum property

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

Step3: Simplify the equation

Combine like - terms: $2x+11 = 137$.

Step4: Solve for $x$

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

Step5: Find $m\angle LMP$ and $m\angle NMP$

$m\angle NMP=x = 63^{\circ}$.
$m\angle LMP=x + 11=63+11 = 74^{\circ}$.

Answer:

$m\angle LMP = 74^{\circ}$
$m\angle NMP = 63^{\circ}$