Question

In triangles ABC and DEF, $\angle A = \angle E$ = 40°, AB : ED = AC : EF and $\angle F$ = 65°, then $\angle B$ =
(a) 35°
(b) 65°
(c) 75°
(d) 85°

Answer 1

Answer:

The measure of ∠B is 75° .

Among the given options option (c) 75° is the correct answer.

Step-by-step explanation:

Given:

In ΔABC &  ΔDEF.

∠A  = ∠E = 40°

∠F = 65°  

AB/ED = AC/EF

In ∆ABC & ∆DEF

∠A = ∠E = 40°    [Given]

AB/ED = AC/EF   [Given]

ΔABC ~ ΔDEF  

[By SAS Similarity criterion]

∠F = ∠C = 65°  

[corresponding angles of a similar triangles are equal ]  

In ∆ABC,  

∠A + ∠B + ∠C = 180°

[By angle sum property of a triangle]

40° + ∠B + 65° = 180°

105° + ∠B = 180°

∠B = 180° - 105°  

∠B = 75°  

Hence, the measure of ∠B is 75° .

HOPE THIS ANSWER WILL HELP YOU ..

Answer 2

Heya!

Refer the attachment!