Q8 of 180 Page 3

In the given fig. DE || BC, ∠ADE =70° and ∠BAC=50°, then ∠BCA = ______


OR


In the given figure, AD = 2cm, BD = 3 cm, AE = 3.5 cm and AC = 7 cm. Is DE parallel to BC ?



By converse of Thale’s theorem DE II BC


∠ADE = ∠ABC = 70°


Given ∠BAC = 50°


∠ABC + ∠BAC + ∠BCA =180° (Angle sum property of triangles)


700 + 500 + ∠BCA = 180°


∠BCA = 180° - 120° = 60°


OR


EC = AC – AE = (7- 3.5) cm = 3.5 cm



So,


Hence, by converse of Thale’s Theorem, DE is not Parallel to BC.


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