Question

In a parallelogram ABCD, if $ \angle A = \dfrac{4}{5}\angle B $ , then what is $ \angle A? $

Answer 1

Hint: In this question we have been told that $ \angle A = \dfrac{4}{5}\angle B $ . So firstly we need to find the value of $ \angle B $ .
We will use the property that the sum of the angles on the side of the line is equal to
 $ {180^ \circ } $ . We can also say this as the nagle angles property of a parallelogram.
By this we will find the value of $ \angle B $ and then we will find $ \angle A $ .

Complete step-by-step answer:
Let us first understand the definition of a parallelogram .
A parallelogram is a quadrilateral with opposite sides parallel and opposite angles are equal. The sum of the adjacent angles of a parallelogram is $ 180^\circ $ , also because their interior angles lie on the same side of the transversal.
Now let us draw the diagram according to the data given in the question:

In the above figure we have a parallelogram i.e. ABCD
We can see that the $ \angle A $ and $ \angle B $ are same side of the line
 $ AB $ .
Now we know the property of parallelogram that the sum of the angles on the side of the line is equal to $ 180^\circ $ .
So we can write that
 $ \angle A + \angle B = 180^\circ $ .
But we have been given that
 $ \angle A = \dfrac{4}{5}\angle B $ .
So by putting this value in the equation we have :
 $ \dfrac{4}{5}\angle B + \angle B = 180^\circ $ .
We will now add the values,
 $ \dfrac{{4\angle B + 5\angle B}}{5} = 180^\circ $
 $ \dfrac{{9\angle B}}{5} = 180^\circ $
By cross multiplication we can write that
 $ \angle B = \dfrac{{{{180}^ \circ } \times 5}}{9} $
On simplifying it gives us value
 $ \angle B = {100^ \circ } $
We can put this value in $ \angle A $ i.e.
 $ \angle A = \dfrac{4}{5} \times 100^\circ $
It gives us
 $ \angle A = 20 \times 4 = {80^ \circ } $ .
Hence the required value of $ \angle A $ is $ {80^ \circ } $ .
So, the correct answer is “ $ {80^ \circ } $ ”.

Note: We should know the properties of parallelograms . The area of the parallelogram is base $ \times $ height . We should know that the perimeter of a parallelogram is $ 2 $ ( Sum of adjacent sides length) .The total number of sides and vertices of parallelogram are the same i.e. $ 4 $ .