Question

the measure of two adjacent angles of a parlellogram are in the ration 5:3 find the measure of each of the angkes of the parlellogram
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Answer 1

To find : measure of each angles of parallelogram  

Given : measure of two adjacent angles of a parallelogram are in the ratio $5:3$

Solution :

• Let , given two angles in ratio be $5x$ and $3x$
• We know that , opposite angles of parallelogram are equal . Therefore other two angles of parallelogram must be equal to $5x$ and $3x$ .
• We also know that sum of all interior angels of parallelogram is $360$°

• Therefore, according to given data , we write as  -

         $5x + 5x + 3x + 3x =$ $360$°

• Solving for variable , we get ,

        $16x =$ $360$°

           $x = \frac{360}{16} \\x = 22.5$

• Substituting  the value we get ,

          $5x = 5\times 22.5 =$ $112.5$°

          $3x = 3\times 22.5 =$ $67.5$°

Hence ,measure of each angle of parallelogram is $112.5$°  , $112.5$°, $67.5$° ,

$67.5$° .