Question

1. if m∠lmp is 13 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 $m\angle LMP=x + 13$. Since $m\angle NML=m\angle NMP + m\angle LMP$ and $m\angle NML = 137^{\circ}$, we have the equation $x+(x + 13)=137$.

Step2: Simplify the left - hand side of the equation

Combining like terms, we get $2x+13 = 137$.

Step3: Solve for $x$

Subtract 13 from both sides: $2x=137 - 13$, so $2x = 124$. Then divide both sides by 2: $x=\frac{124}{2}=62$.

Step4: Find $m\angle LMP$

Since $m\angle LMP=x + 13$ and $x = 62$, then $m\angle LMP=62+13 = 75$.

Answer:

$m\angle LMP = 75^{\circ}$
$m\angle NMP=62^{\circ}$