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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

This is required descending order

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