Question

In a parallelogram ABCD, A:D= 1:2 , find the angles of the parallelogram

Answer 1

Answer:

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Let ABCD be a parallelogram in which ∠A=65∘.

Since AD∥BC we can treat AB as a transversal. So,

∠A+∠B=180∘

65∘+∠B=180∘

∠B=180∘−65∘

∠B=115∘

Since the opposite angles of a parallelogram are equal, we have

∠C=∠A=65∘ and ∠D=∠B=115∘

Hence, ∠B=115∘,∠C=65∘ and ∠D=115∘

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Answer 2

Step-by-step explanation:

In a parallelogram opposite angles are equal

given in the ratio of A:D = 1:2

Opposite angles are equal in a parallelogram

therefore A = C = 1

B= D = 2

sum of angles in a parallelogram = 360°

A+ B+ C+ D= 360

1x+ 2x + 1x + 2x = 360

6x = 360

x = 360÷6

x = 60

<A = <C = 1× 60 = 60

<B = <C = 2 × 60 = 120