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Question
In triangles ABC and DEF, ∠A = ∠E = 40°, AB : ED = AC : EF and ∠F = 65°, then ∠B =
Options
35°
65°
75°
85°
Solution
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°.
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