Question

name ______ date ______ points, lines, rays, and angles name the angles in three different ways

Explanation:

Let's take the first angle (with points A, B, C) as an example to name it in three ways:

Step1: Name by vertex

The vertex of the angle is B, so we can call it $\angle B$.

Step2: Name by three points (with vertex in the middle)

Using points A, B, C (vertex B in the middle), we can call it $\angle ABC$.

Step3: Name by a number (if given, but here we can also use the angle symbol with the vertex)

Alternatively, since it's the angle at B between BA and BC, we can also refer to it as $\angle CBA$ (order of points can be reversed as long as vertex is in the middle).

For the second angle (with points D, E, F):

Step1: Vertex - E

So $\angle E$.

Step2: Three points - $\angle DEF$ (vertex E between D and F)

Step3: Reversed three points - $\angle FED$

For the right angle at J (points L, J, K):

Step1: Vertex - J

$\angle J$ (or $\angle LJK$ or $\angle KJL$), and since it's a right angle, sometimes denoted as $\angle J = 90^\circ$ but for naming, $\angle J$, $\angle LJK$, $\angle KJL$.

For the angle at Y (points X, Y, Z):

Step1: Vertex - Y

$\angle Y$

Step2: $\angle XYZ$

Step3: $\angle ZYX$

For the angle at P (points R, P, Q):

Step1: Vertex - P

$\angle P$

Step2: $\angle RPQ$

Step3: $\angle QPR$

For the angle at S (points S, T, R):

Step1: Vertex - S

$\angle S$

Step2: $\angle TSR$

Step3: $\angle RST$

For the straight line (points T, V, U) - this is a straight angle (180°), named as:

Step1: Vertex - V

$\angle V$

Step2: $\angle TVU$

Step3: $\angle UVT$

For the right angle at C (points A, C, B):

Step1: Vertex - C

$\angle C$

Step2: $\angle ACB$

Step3: $\angle BCA$

For the angle at Y (points W, Y, X):

Step1: Vertex - Y

$\angle Y$

Step2: $\angle WYX$

Step3: $\angle XYW$

For the angle at E (points C, E, D):

Step1: Vertex - E

$\angle E$

Step2: $\angle CED$

Step3: $\angle DEC$

Answer:

(Examples for each angle, taking the first one as a sample full answer)
For the angle with points A, B, C: $\angle B$, $\angle ABC$, $\angle CBA$;
For the angle with points D, E, F: $\angle E$, $\angle DEF$, $\angle FED$;
For the right angle at J (L, J, K): $\angle J$, $\angle LJK$, $\angle KJL$;
For the angle at Y (X, Y, Z): $\angle Y$, $\angle XYZ$, $\angle ZYX$;
For the angle at P (R, P, Q): $\angle P$, $\angle RPQ$, $\angle QPR$;
For the angle at S (S, T, R): $\angle S$, $\angle TSR$, $\angle RST$;
For the straight angle at V (T, V, U): $\angle V$, $\angle TVU$, $\angle UVT$;
For the right angle at C (A, C, B): $\angle C$, $\angle ACB$, $\angle BCA$;
For the angle at Y (W, Y, X): $\angle Y$, $\angle WYX$, $\angle XYW$;
For the angle at E (C, E, D): $\angle E$, $\angle CED$, $\angle DEC$