Question

If an angle of a parallelogram is four - fifths of its adjacent angle, find the angles of parallelogram.

Answer 1

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Answer 2

Given:

We have given the an angle of a parallelogram is four - fifths of its adjacent angle.

To  Find:

We have to find the angles of a parallelogram?

Step-by-step explanation:

• Let one angle of parallelogram is x.
• It is given to us adjacent angle is four-fifth of the angle
• Hence the adjacent angle will be

      $\textrm{4-5th of x}=\frac{4x}{5}$

• Now we know the angle between two transversal lines make the angle of  $180^\circ$.

• Hence we can write for the adjacent angles Sum of angle D and angle C between transversal line will be $180^\circ$

        $x+\frac{4x}{5} =180^\circ$

• Now solve the above equation we will get ( see the attached figure)

        $\frac{5x+4x}{5} =180^\circ\\x=\frac{180\times5}{9} \\x=100$

• Hence the one angle will be$100^\circ$ and the other angle will be calculated as fourth - fifth time

       $\anglec=\frac{4x}{5} =\frac{4\times100}{5} =80^\circ$

• Now we know the opposite angle of a parallelogram are equal hence

        $\angle A=\angle C=80^\circ$

• And also the Other pair of opposite angle will be equal.

       $\angle D =\angle B= 100^\circ$

Hence all the angles of a parallelogram are $80^\circ,100^\circ,80^\circ,100^\circ,$