E is mid-point of side BC of parallelogram ABCD such that CD : AD = 1 : 2. If ∠BAE = 40°, then ∠ADE equals ____
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It is given that ABCD is a parallelogram so we know that AD∥BC.
From the figure, we can identify that ∠DAM and ∠AMB are alternate angles.
⇒∠DAM=∠AMB…(i)
Also, it is given that,
⇒∠BAM=∠DAM…(ii)
From (i) and (ii) we can say that,
∠BAM=∠AMB
By using theorem, Sides opposite to equal angles are equal.
In △ABM,
BM=AB
It is given that M is the midpoint of BC. So,
BM
AB
CD
AD
=
2
1
BC
=
2
1
AD
=
2
1
AD
=2CD
Hence proved.
Step-by-step explanation:
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