Question

In Fig. 10.135, the measure of ∠B’AC’ is
A. 50°
B. 60°
C. 70°
D. 80°

Answer 1

Concept :  

Congruence of triangles :  

• Two triangles are congruent, if sides and angles of a triangle are equal to the corresponding sides and angles of the triangle.  
• In Congruent triangles, corresponding parts are always equal and we write it in short 'CPCT', i e, Corresponding Parts of Congruent Triangles.
• It is necessary to write a correspondence of vertices correctly for writing the congruence of triangles in symbolic form.

 

In ∆ABC and ∆A'B'C',

AB = A'B'  = 6 cm  (Given)

∠B = ∠B'  = 60° (Given)

BC = B'C'   = 5 cm (Given)

Hence, by SAS congruence criterion, we obtain ∆ABC ≅ ∆A'B'C'.

Therefore,

∠A = ∠A' [By CPCT]

Now,  

3x = 2x +20

3x - 2x = 20°

x = 20°

Then,  

∠A' = 2x +20

∠A' = 2 × 20° + 20

∠A' = 40° + 20°

∠A' = 60°

Hence, ∠B'A'C' is 60° .  

Option (B)  60° is correct.

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Similar questions :

If ABC and DEF are two triangles such that Δ ABC≅ Δ FDE and AB =5 cm, ∠B = 40° and ∠A =80°, Then, which of the following is true?

A. DF = 5 cm, ∠F= 60°

B. DE = 5 cm, ∠E= 60°

C. DF = 5 cm, ∠E= 60°

D. DE = 5 cm, ∠D= 40°

https://brainly.in/question/15907780

 

If Δ ABC ≅ Δ LKM, then side of Δ LKM equal to side AC of Δ ABC is

A. LK

B. KM

C. LM

D. None of these

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Answer 2

Answer:

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