Question

If an angle of a parallelogram is two third of its exact angle find the angle of the parallelogram

Answer 1

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Step-by-step explanation:

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If an angle of a parallelogram is two – third of its adjacent angle, find the angles of a parallelogram.

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Hint: We will first start by using the fact that the sum of adjacent angles of a parallelogram is 180∘. Then we will let the one angle of parallelogram as x and according to the question we have the adjacent angle as 23x. Then we will use the fact to find the value of x and similarly other angles.

Complete step-by-step answer:

Now, we have been given that one angle of a parallelogram is 23 of its adjacent. Therefore, we let the one angle of parallelogram as x. Therefore, the adjacent angle is 23x.

Now, we know that the sum of the adjacent angles of a parallelogram is 180∘. Therefore, we have,

x+23x=180∘5x3=180∘x=35×180∘x=3×36∘x=108∘23x=72∘

Now, we know that the opposite angles of a parallelogram are equal. Therefore, we have,

∠ABC=23x=72∘∠BCD=x=108∘

The angles of the parallelogram are 108∘,72∘,108∘,72∘

respectively.

Note: We have used a property of parallelogram that the opposite angles of a parallelogram are equal. Therefore, we have,

∠ABC=∠ADC=72∘∠BAD=∠BCD=108∘

Using this property has helped us to find all the angles of the parallelogram easily.