Question

in the given figure find the measure of angle B'A'C'​

Answer 1

ABC is isosceles. So angle A = angle B = 3x

By angle sum property.

60 + 6x = 180

x = 20

So angle A = angle B = 60

Similarly angle B’A’C = 2x + 20

= 40 + 20 = 60

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Answer 2

Given:

The values of AB, BC, A'B', B'C', ∠B AND ∠B'

To find:

the value of ∠B'A'C'

Solution:

The given triangles ABC and A'B'C' are congruent due to the SAS, Side-Angle-Side Criterion of Congruency. It states that if two sides and the included angle of one triangle are equal to two sides and included angle of another triangle, then the triangles are congruent.

As,

AB = A'B' = 6 cm

∠ABC = ∠A'B'C' = 60°

BC= B'C' = 6 cm

ABC ≅ A'B'C

Hence,

∠BAC  = ∠B'A'C'

But as both these triangles are Isosceles

∠A= ∠C and ∠A' = ∠C'

Using angle sum property,

∠A+ ∠C + ∠B = 180

2∠A  + 60 = 180

2∠A = 120

∠A =  60

∠BAC = 60

As, ABC ≅ A'B'C

Hence, ∠BAC  = ∠B'A'C' = 60°

Therefore the value of ∠B'A'C' is equal to 60°.