Question

in the given figure the value of x is

Answer 1

Step-by-step explanation:

angle x+50=180 [linear pair]

x=180-50

x=130

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,

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

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

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

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

$\bf\implies \:\dfrac{KN}{KM} = \dfrac{PN}{LM}$

$\rm :\longmapsto\:\dfrac{c}{b + c} = \dfrac{x}{a}$

$\bf\implies \:x \: = \: \dfrac{ac}{b + c}$

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MORE TO KNOW

1. Pythagoras Theorem :-

This theorem states that : In a right-angled triangle, the square of the longest side is equal to sum of the squares of remaining sides.

2. Converse of Pythagoras Theorem :-

This theorem states that : If the square of the longest side is equal to sum of the squares of remaining two sides, angle opposite to longest side is right angle.

3. Area Ratio Theorem :-

This theorem states that :- The ratio of the area of two similar triangles is equal to the ratio of the squares of corresponding sides.

4. Basic Proportionality Theorem :-

This theorem states that:- If a line is drawn parallel to one side of a triangle, intersects the other two lines in distinct points, then the other two sides are divided in the same ratio.