Question

In triangles ABC and DEF, ∠A = ∠E = 40°, AB : ED = AC : EF and ∠F = 65°, then ∠B =

Options

• 35°

• 65°

•  75°

• 85°

Answer 1

Given: In ΔABC and ΔDEF

∠A = ∠E = 40°,

AB : ED = AC : EF

∠F = 65°,

To find: Measure of angle B.

In ΔABC and ΔDEF

∠A = ∠E = 4

AB : ED = AC : EF

ΔABC ∼ ΔDEF (S.A.S similarity crieteria)

Hence in similar triangles ΔABC and ΔDEF

∠A = ∠E =40°

∠C = ∠F = 65°

∠B =∠D

We know that sum of all the angles of a triangle is equal to 180°.

∠A + ∠B + ∠C = 180°

40° + ∠B + 65° = 180°

∠B + 105° = 180°

∠B = 180° - 105°

∠B = 75°

Hence, the correct answer is 75°.