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Geometry Reasoning: Angles inside and outside Circles
In this video you will learn how to find the angle measure of angles created inside, and outside circles.
The first problem involves finding an angle using a big ac and the small arc.
The second problem involves using vertical angles.
Finally, the last problem involves linear pairs of angles.
Number 8 We have an angle that is in the circle but it is not in the center and it is not inscribed, so we have to look at the intercepted arcs, add them, and divide by two.
Take 160 + 50 and divide by 2.
This equals 210 and divide by 2 which equals 105.
Therefore angle 8 is 105 and the vertical angle is also 105.
Let's now look at number 9
We have an angle on the outside.
The rule for this one is?
We have a big arc, a small arc, and an exterior angle.
The rule is big arc, minus small arc divided by two equals the angle
I'm going to call this arc we are looking for x
Therefore I will get x-47/2 = 30/1.
Solve by taking a cross product and you get 60 equals x -47
Next, add 47 to both sides and this equals 107.
That means the arc is 107 degrees.
Remember, the big arc minus the small arc equals the angle on the outside of the circle.
Number 10 We have an angle right here, and what kind of angle are we looking for?
Here i the vertex, and the vertex lies on the circle
It is on a tangent line, but notice the vertex is right on the circle.
If this angle is 156 then what do we know about the linear pair?
Linear pairs add to 180 degrees.
I will take 180 minus 156 and that equals 24 degrees.
So 24 is the answer to the problem with the linear pair.
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Tagged under: circles,angles,inscribed,circle arcs,vertical angles,linear pair,geometry,tangent,geometry reasoning
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