Answer:
x=7
Step-by-step explanation:
We are given that
[tex]\angle K=\angle N[/tex]
[tex]\angle J=\angle M[/tex]
Therefore, [tex]\triangle JKL\sim \triangle MNP[/tex]
By AA similarity postulate
AA similarity: When two angles of one triangle are equal to its corresponding angles of other triangle then , two triangles are similar by AA similarity.
When two triangles are similar then the ratio of their corresponding sides are equal.
Therefore, [tex]\frac{JK}{MN}=\frac{JL}{MP}[/tex]
We have JK=25 units,MN=30 units
JL=20 units,MP=[tex]4x-4[/tex]
Substitute the values then we get
[tex]\frac{25}{30}=\frac{20}{4x-4}[/tex]
[tex]\frac{5}{6}=\frac{20}{4(x-1)}=\frac{5}{x-1}[/tex]
[tex]x-1=\frac{5\times 6}{5}[/tex]
[tex]x-1=6[/tex]
[tex]x=6+1=7[/tex]
Hence, the value of x=7
