Q. 7 A

# ABC ↔ DEF is a similarity in ΔABC and ΔADEF, m∠A = 40, m∠E + m∠F =

A. 40

B. 80

C. 140

D. 180

Answer :

Given: m ∠A = 40°

The correspondence ABC ↔ DEF is a similarity between ∆ABC and ∆DEF.

To find: m ∠E + m ∠F = ?

Now by definition, for a given correspondence between the vertices of two triangles, if the corresponding angles of the triangles are congruent and the lengths of the corresponding sides are in proportion, then the given correspondence is a similarity between two triangles.

⇒ m ∠A = m ∠D

⇒ m ∠A = m ∠D = 40°

⇒ m ∠D = 40°

In ∆DEF,

m ∠D + m ∠E + m ∠F = 180°

⇒ 40° + m ∠E + m ∠F = 180°

⇒ m ∠E + m ∠F = 180° - 40°

⇒ m ∠E + m ∠F = 140°

∴ Answer is 140.

**Thus, option (c) is correct.**

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