Question

Using the figure above, if< A  = <D, then< B ___ <E.

Choose the relationship symbol that makes the statement true.

Answer 1

The relationship symbol that makes the statement true is '>'.

Explanation:

Given,

In triangles ABC and EDF,

∠A = ∠D

Since, the sum of all interior angles of a triangle is supplementary,

⇒ ∠A + ∠B + ∠C = 180° and ∠D + ∠E + ∠F = 180°

⇒ ∠A = 180° - ∠B - ∠C and ∠D = 180° - ∠E - ∠F,

By substituting the values,

180° - ∠B - ∠C = 180° - ∠E - ∠F

- ∠B - ∠C = - ∠E - ∠F

∠B + ∠C = ∠E + ∠F

∠B + 20° = ∠E + 30° ( given ∠C = 20° and ∠F = 30° )

∠B = ∠E + 10°

⇒∠B > ∠E

Hence, the relationship symbol that makes the statement true would be '>'.