Question

Given parallelogram JKLM, complete the following statements.

Answer 1

Answer:

m∠K = 43°

Step-by-step explanation:

By the properties of a parallelogram,

1). Opposite sides of a parallelogram are equal and parallel.

   (6y - 13) = 32 - 3y

   6y + 3y = 32 - 13

   9y = 45

   y = 5

2). Consecutive interior angles are supplementary.

   m∠M + m∠J = 180°

   (6x + 17) + (2x + 3) = 180°

   8x + 20 = 180°

    8x = 160°

    x = 20

    m∠M = (2x + 3)°

              = 2(20) + 3

              = 43°

3). Opposite angles of a parallelogram are equal in measure.

   m∠M = m∠K = 43°

Answer 2

Parallelogram is a closed shaped quadrilateral in which the opposite sides are equal and parallel. Consecutive angles in a parallelogram are supplementary. The value of x is 20, the value of the y is 5 and value of the angle K is 43 degrees.

Given-

Length of the  line XL is 2y+23.

Length of the  line Ml  is 32-3y.

Length of the  line JK is 6y-13.

Parallelogram

Parallelogram is a closed shaped quadrilateral in which the opposite sides are equal and parallel. Consecutive angles in a parallelogram are supplementary.

As the sum of the consecutive angles is equal to the 180 degrees (supplementary). Thus,

$\angle J+\angle M=180\\ 6x+17+2x+3=180\\ 8x+20=180\\ x=\dfrac{180-20}{8}\\ x=20$

Thus the value of x is 20.

As the the opposite sides of the parallelogram are equal. Thus,

$\begin{aligned}\\ ML&=JK\\ 32-3y&=6y-13\\ 6y+3y&=32+13\\ 9y&=45\\ y&=\dfrac{45}{9} \\ y&=5\\ \end$

Thus the value of the y is 5.

Opposite angle are equal thus,

$\angle K=\angle M\\ \angle K=2x+3\\ \angle K=2\times20+3\\ \angle K=43$

Thus the value of x is 20, the value of the y is 5 and value of the angle K is 43 degrees.

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