Question

in the figure triangle abc, angle b=35 degree Celsius, angle c= 65 degree Celsius and the bisector of angle bac better bc in x arrange ax,bx,cx in descending order

Answer 1

in angle 

A+B+C= 180
A+35+65=180
A=180-100
A=80  
so angle BAX AND ANGLE CAX =80/2=40
we know that side opposite to the greater angle is longer 
in triangle BAX
BAX(40)>ABX(35)
so BX>AX
in triangle CAX 
ACX(65)>CAX(40)
so AX>CX 
so BX>AX>CX

HOPE IT HELPS MARK BRAINLIEST
THIS IS JOSHUA 9 MERCURY

Answer 2

Given: In ∆ABC, ∠B=35°,∠C=65° and ∠BAX = ∠XAC

To find: Relation between AX, BX and CX in descending order.

In ∆ABC, by the angle sum property, we have

∠A + ∠B + ∠C = 180°

∠A + 35° + 65° = 180°

∠A + 100° = 180°

∴ ∠A = 80°

But ∠BAX =

∠A

=

× 80° = 40°

Now in ∆ABX,

∠B = 35°

∠BAX = 40

And ∠BXA = 180° - 35° - 40°

= 105°

So, in ∆ABX,

∠B is smallest, so the side opposite is smallest, ie AX is smallest side.

∴ AX < BX …(1)

Now consider ∆AXC,

∠CAX =

× ∠A

× 80° = 40°

∠AXC = 180° - 40° - 65°

= 180° - 105° = 75°

Hence, in ∆AXC we have,

∠CAX = 40°, ∠C = 65°, ∠AXC =75°

∴∠CAX is smallest in ∆AXC

So the side opposite to ∠CAX is shortest

Ie CX is shortest

∴ CX <AX …. (2)

From 1 and 2 ,

BX > AX > CX