Answer:
ΔABE ~ ΔCDE by AA criterion .
Option (A) is correct .
Step-by-step explanation:
As given
∠BAE = 45° and ∠CED = 70°
Now in the ΔABE .
By apply angle sum property of a triangles .
∠ABE + ∠BEA + ∠BAE = 180 °
(As ∠BAE = 45° , ∠ABE = 65°)
65 + ∠BEA + 45 = 180 °
∠BEA = 180° - (65+45)°
∠BEA = 180° - 110°
∠BEA = 70°
As in ΔCED .
∠CDE + ∠DEC + ∠ECD = 180°
(As ∠CED = 70° , ∠CDE = 65°)
65 + 70+ ∠ECD = 180°
∠ECD = 180° - (65+70)°
∠ECD = 180° - 135°
∠ECD = 45°
Now in the ΔABE and ΔCDE .
(1) ∠BAE =∠ECD = 45°
(2) ∠BEA=∠CED = 70°
(3) ∠ABE = ∠CDE = 65°
Thus ΔABE ~ ΔCDE by AA criterion .
Option (A) is correct .
