Question

In congruent triangles ABC and DEF, ∠A = ∠D = 40∘, and ∠F = 65∘, then ∠B =?

Answer 1

Question:-

In congruent triangles ABC and DEF, ∠A = ∠D = 40∘, and ∠F = 65∘, then ∠B =?

Answer:-

Given:-

ΔABC ≅ ΔDEF

∠A = ∠D = 40°

∠F = 65°

To find:-

∠B = x (Let value of ∠B be 'x')

Solution:-

As, ΔABC ≅ ΔDEF, all their angles are equal.)

i.e,

∠A = ∠D =40°

∠B =∠E = x

∠C = ∠F = 65°

Therefore, using angles sum properties of triangles,

=> ∠A + ∠B + ∠C = 180°

=> 40° + ∠E + ∠F = 180°

=> 40° + x + 65° = 180°

=> x + 105° = 180°

=> x = 180° - 105°

=> x = 75°

Therefore, ∠B = 75°.

Answer 2

$\sf\Large{\underline{\underline{Question:-}}}$

In congruent triangles ABC and DEF, ∠A = ∠D = 40∘, and ∠F = 65∘, then ∠B =?

$\sf\Large{\underline{\underline{Solution:-}}}$

Given,

↦ ∆ABC ≅ ∆DEF

↦ ∠A = ∠D = 40°

↦ ∠F = 65°

${\bold\blue{To \: find:}}$

• ∠B

${\bold\purple{ATQ,}}$

In ∆DEF,

⇨∠D + ∠E + ∠F = 180°. [Angle sum property]

⇨40° + ∠E + 65° = 180°

⇨∠E + 105° = 180°

⇨∠E = 180° - 105°

⇨∠E = 75°

• We know that, if ∆ABC ≅ ∆DEF so the measure of their angles will be same.

∴ ∠A = ∠D, ∠B = ∠E , ∠C = ∠F

${\bold\pink{Hence,}}$

∠E = ∠B = 75°

∠B = 75°