From ∆ABC and ∆XYZ, the correspondence ABC ↔ YZX is similarity.
Also, m ∠B + m ∠C = 120°
To find: m ∠Y = ?
In ∆ABC, by angle sum property of triangles we can say that,
m ∠A + m ∠B + m ∠C = 180°
⇒ m ∠A + (m ∠B + m ∠C) = 180°
⇒ m ∠A + 120° = 180°
⇒ m ∠A = 180° - 120°
⇒ m ∠A = 60° …(i)
Now, from ∆ABC and ∆XYZ, the correspondence ABC ↔ YZX is similarity.
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.
⇒ ∠A ≅ ∠Y
∴ m ∠A = m ∠Y
From equation (i), we get
m ∠A = m ∠Y = 60°
∴ m ∠Y = 60°
Thus, option (d) is correct.
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