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  • IIt is given that triangleABC cong triangleFDE and AB = 5 cm, angleB = 40° and angleA = 80°. Then which of the following is true?(A) DF = 5 cm,angleF = 60°(B) DF = 5 cm, angleE = 60°(C) DE = 5 cm, angleE = 60°(D) DE = 5 cm, \angleD = 40°

It is given that \triangleABC \cong \triangleFDE and AB = 5 cm, \angleB = 40° and \angleA = 80°. Then which of the following is true?

(A) DF = 5 cm, \angleF = 60°

(B) DF = 5 cm, \angleE = 60°

(C) DE = 5 cm, \angleE = 60°

(D) DE = 5 cm, \angleD = 40°

Answers (1)

[B]

Solution.         In \triangleABC, \angleA = 80°, \angleB = 40° and  \angleC = x  ( assume)

\because \angleA + \angleB + \anglex = 180° (angle sum property of a triangle)

\Rightarrow 80° + 40° + x = 180°

\Rightarrow x = 180° – 120°

\Rightarrowx = 60°

\Rightarrow ÐC = 60°

\because \triangleABC \cong \triangleFDE

By ASA congruence relation

AB = FD, \angleA = \angleF, \angleB = \angleD

\Rightarrow DF = 5 cm, \angleF = 80°, \angleB = 40° = \angleD

\because Also, \angleC = \angleE

\Rightarrow\angleE = 60°

Therefore, DF = 5 cm, \angleE = 60°

Hence option (B) is correct.

 

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