Question

1) The measure of two adjacent angles of a parallelogram are in the ratio 3.2 . Find the measure of each of the angle of the parallelogra .



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Answer 1

Answer:

$\bigstar{\bold{Angle\:P=108^{o} }}$

$\bigstar{\bold{Angle\:Q=72^{o} }}$

$\bigstar{\bold{Angle\:R=108^{o} }}$

$\bigstar{\bold{Angle\:S=72^{o}}}$

Step-by-step explanation:

$\Large{\underline{\underline{\bf{Given:}}}}$

• Adjacent angles are in the ratio 3 : 2

$\Large{\underline{\underline{\bf{To\:Find:}}}}$

• The measure of each angle of the parallelogram

$\Large{\underline{\underline{\bf{Solution:}}}}$

↬ Here we have to find each angle of the parallelogram

↬ Let the 4 angles of the parallelogram be P, Q, R , S

↬ Let Angle P = 3 x

↬ Let Angle Q = 2 x

↬ We know that in a parallelogram,

    Sum of Adjacent angles = 180

↬ Hence,

    Angle P + Angle Q = 180

    3x + 2x = 180

    5x = 180  

      x = 36

↬ Substituting the value of x

↬ Angle P = 3 × 36

   Angle P = 108°

   $\boxed{\bold{Angle\:P=108^{o} }}$

↬ Now finding Angle Q

   Angle Q = 2x

   Angle Q = 2 × 36

   Angle Q = 72

  $\boxed{\bold{Angle\:Q=72^{o} }}$

↬ Now we know that opposite angles are equal in a parallelogram

↬ Hence,

   Angle P = Angle R

   Angle R  =108°

   $\boxed{\bold{Angle\:R=108^{o} }}$

↬ Also,

    Angle Q = Angle S

    Angle S = 72°

    $\boxed{\bold{Angle\:S=72^{o}}}$

$\Large{\underline{\underline{\bf{Notes:}}}}$

↬ In a parallelogram

• Opposite sides are parallel and equal
• Opposite angles are equal
• Adjacent angles are supplementary