In a triangle ABC, D, E and F are points on AB, BC and CA respectively such that DE = BE and EF = EC. If angle A is 40 degrees then what is angle DEF in degrees?
Explanation:
Since DE = BE, ⇒ ∠DBE = ∠BDE = x (say)
Since EF = EC, ⇒ ∠EFC = ∠ECF = y (say)
Hence, ∠DEB = 180°– 2x and ∠FEC = 180°– 2y.
⇒ ∠DEF = 180° - ∠DEB - ∠FEC
⇒ ∠DEF = 180° - (180 – 2x) – (180 – 2y)
⇒ ∠DEF = 2(x + y) - 180
Also, a + b + 40° = 180° or a + b = 140°.
∴ ∠DEF = 2 × 140 – 180 = 100°
Hence, 100.
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