Question

2. What is the value of x? Show your work.

Answer 1

x=7

Explanation:

We are given that

`\angle K=\angle N`

`\angle J=\angle M`

Therefore,
`\triangle JKL\sim \triangle MNP`

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,
`(JK)/(MN)=(JL)/(MP)`

We have JK=25 units,MN=30 units

JL=20 units,MP=
`4x-4`

Substitute the values then we get

`(25)/(30)=(20)/(4x-4)`

`(5)/(6)=(20)/(4(x-1))=(5)/(x-1)`

`x-1=(5* 6)/(5)`

`x-1=6`

`x=6+1=7`

Hence, the value of x=7