ABCD is a quadrilateral
calculate the value of x

A. x = 18

B. Line AD and line BC are parallel.

Step-by-step explanation:

A. Determination of the value of x.

5x + 3x + 7x + 90 = 360 (sum of angles in quadrilateral.

15x + 90 = 360

Collect like terms

15x = 360 – 90

15x = 270

Divide both side by 15

x = 270/15

x = 18

B. Determination whether or not line AD will be parallel to line BC if drawn to scale.

We shall determine the various angle in the quadrilateral. This can be obtained as follow:

<A = 5x

x = 18

<A = 5(18)

<A = 90°

<B = 90°

<C = 7x

x = 18

<C = 7(18)

<C = 126°

<D = 3x

x = 18

<D = 3(18)

<D = 54°

Summary:

<A = 90°

<B = 90°

<C = 126°

<D = 54°

From the above illustration, we can see that <A and <B are equal (i.e 90°). Thus, line AB is a perpendicular bisector of line AD and line BC. This implies that the distance between line AD and BC are the same at every point. Therefore, line AD and line BC are parallel.