The middle letter of an angle must be its vertex, so the vertex ofis.

An angle can be named after its vertex alone as long as it is the only angle with that vertex. This is not the case here, socannot be correct. Also,andare incorrect since the middle letters are not.

The first and last letters of a three-letter angle name must be points on different sides of the angle.is incorrect sinceandare on the same side of the angle. The correct choice is therefore, sinceandare on different sides of the angle.

A triangle can be named after its three vertices in any order. Since the vertices of the triangle are, any name that includes these three letters is valid. All of the choices fit this description.

An angle can be given a name with three letters if the middle letter is the name of the vertex and the other two letters denote points on different sides of the angle. All four of the three-letter choices fit this description.

An angle can be given a one-letter name if the letter is the name of the vertexandif it is the only angle shown in the diagram to have that vertex (thereby avoiding ambiguity). There are four angles in the diagram with vertex, so we cannot useto indicate any of them, including.is the correct choice.

Two angles form a linear pair if they have the same vertex, they share one side, and their interiors do not intersect.has vertexand sidesand;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 endpointsand, 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 oppositeand, 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 resultingvalue back in to one of the equations and solve for.

Addto both sides and subtractfrom both sides to isolate our like terms:

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

So, thevalue 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 whenis equal toand—in this case,and—is equal to.