1.

In a parallelogram ABCD, the side DC is produced to E and ∠BCE = 105° calculate ∠A,∠E,∠C and∠D.

Answer»

∠DCB + ∠DCE = 180° [Linear pair] 

∠DCB + 105° = 180° 

∠DCB = 180° – 105° 

∠DCB = 75° 

∠A = ∠DCB = 75° 

∠A =∠C = 75° 

[Opposite angles of a parallelogram] 

∠A +∠B = 180° 

[adjacent angles of a parallelogram] 

75° +∠B = 180° 

∠B = 180° + 75° 

∠B = 105° 

∠B = ∠D = 105° 

[Opposite angles of a parallelogram]



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