Question

In the given figure find the value of x.​

Answer 1

قيمة x تساوي أربعين

أتمنى أن يساعد :)

Answer 2

`\large\underline{\sf{Solution-}}`

Given that,

→ In triangle KML, P and N are the points on KK and KM respectively such that

`\rm \longmapsto\:KN = c`

`\rm \longmapsto\:NM = b`

`\rm \longmapsto\:PN = x`

`\rm \longmapsto\:LM = a`

`\rm \longmapsto\: \angle \: KNP = 50 \degree`

`\rm \longmapsto\: \angle \: LKM = 50 \degree`

Now,

`\rm \longmapsto\: In \: \triangle \: LKM \: and \: \triangle \:KNP`

`\purple{\rm \longmapsto\:\angle \:PKN \: = \: \angle \:PKN \: \: \: \: \: \{common \}}`

`\purple{\rm \longmapsto\:\angle \:KNP \: = \: \angle \:KML \: \: \: \: \: \{each \: 50 \degree \}}`

`\purple{\rm\implies \:\triangle \:LKM \: \sim \: \triangle \:PKN \: \: \: (AA \: similarity)}`

`\bf\implies \:(KN)/(KM) = (PN)/(LM)`

`\rm \longmapsto\:(c)/(b + c) = (x)/(a)`

`\bf\implies \:x \: = \: (ac)/(b + c)`

`\textsf{Hope this helps!!}\\`