Question

e is mid-point of side bc of parallelogram abcd such that cd: ad = 1:2. if angle eab = 40°, then angle ade equals​

Answer 1

Given : e is mid-point of side bc of parallelogram abcd such that cd: ad = 1:2. if angle eab = 40°,  

To Find : angle ade

Solution:

cd: ad = 1:2

cd = k  then ad = 2k

ab = cd = k

bc = ad = 2k

e is the mid point of bc

=> be = ce = 2k/2 = k

ab = be = k

=> ∠eab  = ∠aeb = 40°

∠eab  +  ∠aeb + ∠abe  = 180°  triangle angle sum

=> ∠abe = 100°

=> ∠adc = 100°  ( opposite angles of parallelogram)

∠abe + ∠dce = 180°    adjacent angles of parallelogram

=> ∠dce   =  80°

∠cde = ∠ced   as cd = ce = k

∠cde +  ∠ced + ∠dce = 180°

=> ∠cde  = 50°

∠adc = 100°

∠cde  = 50°

∠ade = ∠adc - ∠cde  

=  100° - 50°

= 50°

Hence angle ade  is 50°

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