9514 1404 393
1. vertex: J, sides: JH and JK
5. angle 3, angle M, angle LMN, angle NML
10. angles 1, 3, 6, HVJ, HVK, HVL, JVK, JVL, KVL, JVH, KVH, LVH, KVJ, LVJ, LVK
Step-by-step explanation:
Your question has too many parts for the kind of answers is intended to provide. So, we hope to alleviate your confusion by providing examples of the way these questions are answered.
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An angle can be named by any of ...
its vertexan angle designator in an unambiguous place (usually inside, near the vertex)three points, with the vertex listed in the middle
Note that angle ABC consisting of rays BA and BC sharing end point B can also be named angle CBA.
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1. The rays share end point J. That is the vertex of the angle. The rays are named using the end point first, so the rays in this diagram are JH and JK.
The vertex is J; the sides are JH and JK.
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5. We note there is an angle designator inside near the vertex, point M. That designator can be used to name the angle: angle 3.
There are only two rays that meet at vertex M, so the angle can also be named by naming the vertex: angle M.
The angle can also be named by naming an point on each ray, with the vertex in the middle: angle LMN or angle NML.
The four ways to name this angle are: angle 3, angle M, angle LMN, angle NML.
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10. All of the angles with numeric designators have V as a vertex. Those angles are angle 3, angle 1, angle 6.
In this case, we cannot use V to name an angle, because many angles have vertex V. That name would be ambiguous, not referring to a specific angle.
The other angles that have V as a vertex can be named by naming their rays. There are 4 rays that meet at vertex V. Any two will identify an angle. There are 4·3 = 12 permutations of 4 rays taken 2 at a time. For example, if we choose to use rays VJ and VK as the two rays of our angle, we can name it two ways: JVK or KVJ. (This particular angle is also angle 1.)
So, the angles that have V as a vertex are ...
angles HVJ, HVK, HVL, JVK, JVL, KVL, JVH, KVH, LVH, KVJ, LVJ, LVK
