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.

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

answer is (b.

164 ft2)

a base  

18

b base  

7

h height  

8

isocolese triangle

we know that the line connect a and b is the hyptonuse

so first find the hypotonuse length using the distance formula, call the length c

since it is an isocolese triangle, the lengths of the legs are the same

using pythagorean theorem,

in this case, a=b since isocolese triangle so we get

or

we can find c so we can find the distances

we know that if we draw 2 circles, each has center at a and b, and find where they intersect, we can the 2 possible locations for c

if a has center at (xa,ya) and b has center at (xb,yb), then we can solve where

and

intersect to find where they intersect

i'm not going to put an example because i have to go to class. i hope this explanation is enough