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Angles: Types and Labeling - Problem 1
There is some basic knowledge about angles that needs to be defined. Angles are congruent if they have the same measure, or degrees of the angle. Angles are adjacent if they share a common vertex and a common side. Remember that an angle's vertex is always the point when writing out the angle. For example, ∠XYW and ∠WYZ have a common vertex, Y. They are also adjacent, since they both have the common side YW or WY. The sum of two adjacent angles is the sum of the overall angle formed by the sum of the smaller angles. So, m∠XYW + m∠WYZ = m∠XYZ.
In this drawing how many angles are there? Well if we look at the two obvious ones we have this angle right here which we could say is angle XYW notice that I use Y my vertex is my middle letter I also have this angle I’m trying to mark with two different markings, WYZ.
And I have a third angle which encompasses the two angles so that’s going to be XY and Z we going to have angle forgot my angle symbol XY and Z. So a couple of interesting things first is these two angles the two smaller ones are considered to be adjacent which means they share a common and point a common vertex and a common side which will be ray YW.
They also if I sum them, if I add them so I guess I can call this angle one angle two and then this big one angle three. I can say that angle one plus angle two is equal to angle three. Now what about congruent angles? If I have two angles whose measure is the same so let’s say I measure these and these were both 550.
Then I could say that the measure of angle LMN is equal to the measure so that lower case m next to the angle means measure of OPQ and since the measures are the same then we can conclude that angle LMN is congruent to angle OPQ. And the way that you mark congruent angles there is two different ways depending on your text book one way if I erase this is just using the same number of arcs so if I use two arcs in this angle and two arcs in that angle it is implied that those are congruent.
Now the other method that you might see is that you always use one arc but you are going to use a different number of markings that intersect the arc. So if I add two arcs from both of these that would tell you the geometry student that these two angles must be congruent.
So when you see this m that means measure and after the measure of two angles arc are equal to each other than the angles are congruent, and the second key thing remember is that the sum of two angles that are adjacent is going to be equal to the overall angle formed by the sum of the two small angles.