Question

7 fill in the blank 2 points if (mangle lmp) is 11 degrees more than (mangle nmp) and (mangle nml = 137), find each measure.(mangle lmp=) type your answer... (mangle nmp=) type your answer...

Explanation:

Step1: Set up equations

Let $m\angle NMP = x$. Then $m\angle LMP=x + 11$. Since $\angle NML=\angle NMP+\angle LMP$ and $m\angle NML = 137$, we have the equation $x+(x + 11)=137$.

Step2: Simplify the equation

Combining like - terms in $x+(x + 11)=137$, we get $2x+11 = 137$.

Step3: Solve for $x$

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

Step4: Find $m\angle LMP$

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

Answer:

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