Mathematics
If in triangles ABC and DEF, ∠A = ∠E = 40°, AB : ED = AC : EF and ∠F = 65°, then ∠B is equal to :
35°
65°
75°
85°
Answer
Given,
ΔABC and ΔDEF
∠A = ∠E = 40° [Equal angles]
AB : ED = AC : EF [Corresponding sides are equal]
∴ ΔABC ∼ ΔEDF by SAS similarity. Therefore,
⇒ ∠A = ∠E = 40°
⇒ ∠B = ∠D = x
⇒ ∠C = ∠F = 65°
The sum of all the angles in a triangle is 180°:
⇒ ∠A + ∠B + ∠C = 180°
⇒ 40° + x + 65° = 180°
⇒ x = 180° - 40° - 65°
⇒ x = 75°
⇒ ∠B = ∠D = 75°.
Hence, option 3 is the correct option.
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