Question

1. if m∠lmp is 11 degrees more than m∠nmp and m∠nml = 137°, find each measure. m∠lmp = __ m∠nmp = __

Explanation:

Step1: Set up variables

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

Step2: Use angle - addition postulate

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

Step3: Simplify the equation

Combining like - terms gives $2x+11 = 137$.

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:

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