Two angles form a linear pair if they have the same vertex, they share one side, and their interiors do not intersect.  has vertex  and sides  and ;  has vertex , shares side , and shares no interior points, so this is the correct choice.

A line segment is named after its two endpoints in either order;  is the segment with endpoints  and , so it can also be named . 

Two angles are vertical if they have the same vertex and if their sides form two pairs of opposite rays. The correct choice will have vertex , which is the vertex of . Its rays will be the rays opposite  and , which, are, respectively,   and , respectively. The angle that fits this description is . 

To find where two lines intersect, simply set them equal to each other and solve for . Then plug the resulting  value back in to one of the equations and solve for .

Add  to both sides and subtract  from both sides to isolate our like terms:

So,  must be true for where these lines intersect. Next, plug  back in for  in one of our original equations:

So, the  value of our intersection is .

This makes the coordinate of our intersection .

You can check your answer by plugging in the point you calculated into both equations. Both equations will be true when  is equal to  and —in this case,  and —is equal to .

The perimeter is the sum of the measures of the sidelengths.

Knowing that the hexagon is regular only tells you the six sides are congruent; without the measure of any side, this does not help you. 

Knowing only that each of the six sides measures 10 cm is by itself enough to calculate the perimeter to be

.

The answer is that Statement 1 is sufficient, but not Statement 2.

This figure can be seen as a smaller rectangle cut out of a larger one; refer to the diagram below.

We can fill in the missing sidelengths using the fact that a rectangle has congruent opposite sides. Once this is done, we can add the lengths of the sides to get the perimeter:

 feet.

The perimeter  of any figure is the sum of the lengths of its sides. Since we have a rectangle with a length of  and a width of , we know that there will be two sides of length  and two sides of width . Therefore:

In order to find the perimeter  of the right triangle, we need to know the lengths of each of its sides. While we are given two sides - the base  and the height  - we do not know the hypotenuse . There are two ways that we can find , the first of which is the direct application of the Pythagorean Theorem: 

We could have also noted that  is a common Pythagorean Triple and deduced the value of  that way.

Now that we have all three side lengths, we can calculate :

Starting with the knowledge that we are dealing with an octagon, an 8-sided figure, we calculate the perimeter  by adding the lengths of all 8 sides. Since we also know that each side measures , we can use multiplication:

A pentagon is a 5 sided shape. We are given that two sides are 5 inches each.

Side 1 = 5inches

Side 2 = 5 inches

The next two sides are each 1.5 times bigger than the smallest two sides.

Side 3 =Side 4= 7.5 inches

The last side is twice the size of the smallest side, 

Side 5 =10 inches

Add them all up for our perimeter:

5+5+7.5+7.5+10=35 inches long