Question

SOLVE THE FOLLOWING & CHUUUL
1. The opposite angles of a parallelogram are (3x + 5)º and (61 - x)". Then
the measure of four angles- *​

Answer 1

Answer:

$\bigstar{\bold{Angle\:A=47^{o} }}$

$\bigstar{\bold{Angle\:B=133^{o} }}$

$\bigstar{\bold{Angle\:C=47^{o} }}$

$\bigstar{\bold{Angle\:D=133^{o} }}$

Step-by-step explanation:

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

• Opposite angles are (3x + 5)° and (61 - x)°

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

• Measure of 4 angles of the parallelogram

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

➢ Here we are given the opposite angles of a paralellogram.

➢ Let the angle be A, B, C, D

➢ First we have to find the value of x

➢ We know that in a parallelogram, opposite angles are equal.

➢ Hence,

   3x + 5 = 61 - x

   3x + x = 61 - 5

   4x = 56

     x = 56/4

    x = 14

➢ Hence the value of x is 14

➢ Therefore Angle A is given by,

    Angle A = 3 x + 5

    Angle A = 3 × 14 + 5

    Angle A = 42 + 5

    Angle A = 47°

   $\boxed{\bold{Angle\:A=47^{o} }}$

➢ Now we know that in a parallelogram, adjacent angles are supplementary.

➢ Angle A + Angle B = 180

   Angle B = 180 - 47

   Angle B = 133°

  $\boxed{\bold{Angle\:B=133^{o} }}$

➢ Angle C is given by,

   Angle C = 61 - x

   Angle C = 61 - 14

   Angle C = 47°

   $\boxed{\bold{Angle\:C=47^{o} }}$

➢ Angle D = Angle B

    Angle D = 133

    $\boxed{\bold{Angle\:D=133^{o} }}$

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

➢ In a parallelogram,

• Opposite angles are equal
• Adjacent angles are sullplementary