Question

1. if m∠lmp is 111 degrees more than m∠nmp and m∠nml = 137°, find each measure. m∠lmp = m∠nmp =

Explanation:

Step1: Set up an equation

Let $m\angle NMP = x$. Then $m\angle LMP=x + 11$. Since $m\angle NML=137^{\circ}$ and $\angle NML=\angle NMP+\angle LMP$, 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: $x=\frac{126}{2}=63$.

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

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

Answer:

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