Question

i dont know how to do this geometry especially the first question please help!

Answer 1

Notice that angles JNM, KNP and MNP are supplementary, then we have:

$\begin{gathered} 10x+3+7x+2+90=180 \\ \Rightarrow17x+95=180 \\ \Rightarrow17x=180-95=85 \\ \Rightarrow x=\frac{85}{17}=5 \\ x=5 \end{gathered}$

with x =5, we can find the measure of angle JNM and angle KNP:

$\begin{gathered} \measuredangle JNM=7(5)+2=37 \\ \measuredangle KNP=10(5)+3=53 \end{gathered}$

next, notice that angles JNM and LNK are vertical angles, then:

$\measuredangle LNK=37$

next, angle LNK and angle JNL are supplementary, then:

$\measuredangle JNL=143$

finally, angle JNP is the sum of angle JNM and the right angle MNP, then:

$\measuredangle JNP=37+90=127$

therefore:

KNP=53

LNK=37

JNL=143

JNP=127