Question

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

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 $m\angle NML = 137$, we have the equation $x+(x + 11)=137$.

Step2: Simplify the left - hand side of the equation

Combining like terms, $x+x+11 = 2x+11$. So the equation becomes $2x+11 = 137$.

Step3: Solve for $x$

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

Step4: Find $m\angle LMP$ and $m\angle NMP$

Since $x = m\angle NMP$, then $m\angle NMP=63$. And $m\angle LMP=x + 11=63+11 = 74$.

Answer:

$m\angle LMP = 74$
$m\angle NMP = 63$