Question

In a triangle ABC angle BCA=90. Points E and F lie on the hypotenuse AB such that AE=AC and BF=BC Find angle ECF.
EXPLAIN

Answer 1

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Answer 2

Answer:

Given, ∠C = 90°As angles opposite to equal sides of a ∆ are equal, so∠1 =∠2   ( Since, BF = BC)∠3 =∠4   ( Since, AE = AC)Now, ∠ECF = ∠2+∠4 -∠C..........(i)Now, in ∆ECF∠1 +∠3 + ∠ECF = 180°⇒∠1 +∠3 +-∠C =180° (from (i))⇒2∠2+2 ∠4  = 180° +90°⇒∠2+∠4 =135°.......(ii)∠ECF = 135°-90°=45°

Step-by-step explanation:

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