Question

The top of Lucy's dining table is parallel to the floor as shown, using the two marked angles, write and solve an equation to find the value of x. please show step by step instructions.

Answer 1

Answer: G. x = 11

Step-by-step explanation:

The diagram of the table is shown in the attached photo for better illustration.

Referring to the diagram,

Angle 13x + 12 and angle y are on a straight line. Since the sum of the angles on a straight line is 180 degrees, it means that

y + 13x + 12 = 180

y = 180 - 12 - 13x

y = 168 - 13x- - - - -1

Since the top and the bottom are parallel lines, then angle y and angle 2x + 3 are alternate angles. Alternate angles are equal. Therefore

y = 2x + 3- - - - - 2

Equating equation 1 to equation 2, it becomes

168 - 13x = 2x + 3

2x + 13x = 168 - 3

15x = 165

x = 165/15

x = 11