If ∠bae = 45° and ∠ced = 70° is δabe ~ δcde? if so, by what criterion?
a) yes, by aa criterion
b) yes, by sas criterion
c) yes, by ssa criterion
d) no, not possible to tell.

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 .

the answer is 40.

proof:

just took the test and my answers down below!

step-by-step explanation:

check the pic :