Question

In triangles ABC and DEF , angle A = angle E = 40 , AB : ED = AC : Ef and angle F = 65 , then angle B = ?

Answer 1

Step-by-step explanation:

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°