Question

Can you help me find x :,) please​

Answer 1

as Sides are equal so ,

6x+1= 9x-23 (corresponding angles)

3x= 24

x= 8

Answer 2

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

☆ Let name the triangle as JKL and let MN be the intersecting line meets JK at M and KL at N.

Now,

Given that

In triangle JKL,

• KM = MJ

i.e. M is the midpoint of KJ.

• NK = NL

i.e. N is the midpoint of KL.

And

• ∠KMN = (6x + 1)°

• ∠KJL = (9x - 23)°

We know,

Midpoint Theorem

It states that

Line segment joining the mid-points of two sides of a triangle is parallel to third side and equals to half of it.

So,

According to statement,

• M is the midpoint of KJ

• N is the midpoint of KL.

Hence,

By midpoint theorem,

$\rm :\longmapsto\:JL \: \parallel \: MN$

$\rm :\longmapsto\: \angle \: KJL \: = \: \angle \: KMN \: \: \: \{corresponding \: angles \}$

0

$\rm :\longmapsto\:9x - 23 = 6x + 1$

$\rm :\longmapsto\:9x - 6x= 23 + 1$

$\rm :\longmapsto\:3x= 24$

$\bf\implies \:x = 8$

Additional Information :-

Converse of Midpoint theorem :-

If a line is drawn through the midpoint of one side of a triangle parallel to other side, it bisects the third side.