In the adjoining figure, it is given that CE || BA, ∠BAC = 80° and ∠ECD = 35°.
Find (i) ∠ACE, (ii) ∠ACB, (iii) ∠ABC.

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Solution

$Given : CE ∥ BA ∠ BAC = 80 °, ∠ ECD = 35 ° (i) ∠ BAC = ∠ ACE = 80 ° (alternate angles with AC as a transversal) (ii) ∠ ACB + ∠ ACD = 180 ° (linear pair) or ∠ ACB + ∠ ACE + ∠ ECD = 180 ° or ∠ ACB + 80 ° + 35 ° = 180 ° or ∠ ACB = 65 ° (iii) In ∆ ABC : ∠ BAC + ∠ ACB + ∠ ABC = 180 ° (angle sum property) 80 ° + 65 ° + ∠ ABC = 180 ° ∠ ABC = 35 °$

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