### Video Transcript

Does the ordered pair given by the
ray joining πΆπ΄ and the ray joining πΆ to π· express an angle in standard
position?

We know that for an angle to be in
standard position, its vertex must be centered at the origin and the initial side
must lie on the positive π₯-axis. Now, our angle is defined by this
ordered pair. So we have the ray joining πΆ and
π΄ and the ray joining πΆ and π·. The ray joining πΆ to π΄ is this
one, and that does indeed lie on the positive π₯-axis. We know itβs the initial side of
our angle because itβs mentioned first. Then the ray that joins πΆ to π· is
this one here, meaning the angle weβre interested in is this one. But does the vertex of this lie at
the origin? Well, no, the vertex is over here
somewhere. Itβs someway along the positive
π₯-axis. And so the ordered pair defined by
the ray joining πΆ to π΄ and the ray joining πΆ to π· does not express an angle in
standard position. And the answer is no.

There are, however, a couple of
angles that are in standard position here. The first would be given by the
ordered pair the ray joining π to πΆ and the ray joining π to πΈ. The ray ππΆ lies on the positive
π₯-axis, and then the vertex is centered at the origin. Similarly, we could begin with the
same initial side, and thatβs the ray joining π to πΆ, and measure through to the
ray joining π to πΊ. The vertex for this angle is still
located at the origin, and so the angle is also in standard position.