Q. 383.8( 6 Votes )

# In ∆ABC, ∠B=35°,∠C=65° and the bisector of ∠BAC meets BC in X. Arrange AX, BX and CX in descending order.

Answer :

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

Rate this question :

Each question consists of two statements, namely, Assertion (A) and Reason (R). Please select the correct answer.

In the given figure, PQ>PR and QS and RS are the bisectors of ∠Q and ∠R respectively. Show that SQ>SR

RS Aggarwal & V Aggarwal - Mathematics

In, if -=42°and-=21°, Find,and.

RS Aggarwal & V Aggarwal - MathematicsOf the three angles of a triangle, one is twice the smallest and mother one is thrice the smallest. Find the angle.

RS Aggarwal & V Aggarwal - MathematicsOf the three angles of a triangle are equal and the third angle is greater than each one of them by 18°. Find the angle.

RS Aggarwal & V Aggarwal - MathematicsTwo adjacent angles on a straight line are in the ratio 5:4 Find the measure of each one of these angles.

RS Aggarwal & V Aggarwal - MathematicsIn the given figure, ABC is a triangle in which::=3:2:1 and AC CD. Find the measure of.

RS Aggarwal & V Aggarwal - Mathematics

In ∆ABC, ∠B=35°,∠C=65° and the bisector of ∠BAC meets BC in X. Arrange AX, BX and CX in descending order.

RS Aggarwal & V Aggarwal - Mathematics

In ∆ABC, side AB is produced to D such that BD=BC. If ∠B=60° and ∠A=70°, prove that (i) AD>CD and (ii) AD>AC.

RS Aggarwal & V Aggarwal - Mathematics

In ∆ABC, if ∠A=36° and ∠B=64°, name the longest and shortest sides of the triangle.

RS Aggarwal & V Aggarwal - Mathematics