Give the value of x in each quadrilateral. Then state if the quadrilateral is a Trapezoid. Why/why not? (Hint: Shapes are not drawn to scale)

Let's focus on the figure on the left.

For any quadrilateral, the angles always add up to 360. We'll use this to find x.

105+80+75+x = 360

260+x = 360

x = 360-260

x = 100

Now notice that the pair of adjacent angles 105 and 80 add up to 105+80 = 185, which is not 180. Similarly, the adjacent angles 80 and 75 add to 155 which is not 180.

This is enough to show that we don't have any parallel lines here. If we did have parallel lines, then adjacent angles would add to 180.

Since none of the lines are parallel, this figure is not a trapezoid

Any trapezoid has exactly one pair of parallel lines.

Move onto the figure on the right

We'll follow the same ideas mentioned in the last section.

x+110+92+88 = 360

x+290 = 360

x = 360-290

x = 70

Note how the adjacent angles 70 and 110 add to 70+110 = 180. This shows they are supplementary angles and that we do have a set of parallel lines (top and bottom). In contrast, the angles 110 and 92 do not add to 180, so that helps us see we only have one pair of parallel lines.

Therefore, the figure is a trapezoid

2/3x + 7 = 29

step-by-step explanation:

two thirds = 2/3

plus a number = x

at least 29 = 29

there for you should get 2/3x + 7 = 29