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8th
Maths
Understanding Quadrilaterals
Some Special Parallelograms
ABCD is a rhombus and ABDE ...
MATHS
ABCD is a rhombus and ABDE is a parallelogram.
Given that EDC is a straight line and ∠AED=36
o
, find ∠BAD.
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⇒ ∠BDC = ∠AED = 36
∘
( corresponding angles of AE and BD.)
⇒ We know that ABCD is a rhombus, so AB∥DC
⇒ ∠ABD = ∠BDC =36
∘
( Alternate angles)
⇒ ∠ADB = ∠ABD = 36
∘
(Base angles of isosceles, since AB =DC)
⇒ In △ADB,
⇒ ∠BAD + ∠ABD + ∠ADB = 180
∘
Substituting all the values we get,
⇒ ∠BAD + 36
∘
+ 36
∘
= 180
∘
⇒ ∠BAD = 180
∘
- 36
∘
- 36
∘
∴ ∠BAD = 108
∘
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