Given in triangles ABC and DEF, ∠A = ∠E = 40°, AB: ED = AC: EF and ∠F = 65°.
We know that SAS similarity criterion states that if one angle of a triangle is equal to one angle of the other triangle and the sides including these angles are proportional, then the two triangles are similar
In ΔABC and ΔDEF,
∠A = ∠E and AB: ED = AC: EF then ΔABC ~ ΔDEF
So,
∠A = ∠E = 40°
⇒ ∠C = ∠F = 65°
Similarly, ∠B = ∠D
We know that the sum of all angles of a triangle is equal to 180°.
⇒ ∠A + ∠B + ∠C = 180°
⇒ 40° + ∠B + 65° = 180°
⇒ ∠B + 115° = 180°
⇒ ∠B = 180° - 115° = 75°
∴ ∠B = 75°
