Angles in Circles formed by Tangents, Chords, Secants
Assume the lines that appear tangent are tangent, find the value of x.
x =
degrees
Assume the lines that appear tangent are tangent, find the value of x.
x =              degrees
Assume the lines that appear tangent are tangent, find the value of x.
x =           degrees
Determine whether a tangent line is shown.
Yes
No
Not enough information

Find the angle measure indicated. Assume that lines which appear to be

tangent are tangent.

90º
?
114º
?
33º
?

Find the angle measure indicated. Assume that lines which appear to be

tangent are tangent.

34º
?
90º
?
º

Find the angle measure indicated. Assume that lines which appear to be

tangent are tangent.

º
º
º

Find the angle measure indicated. Assume that lines which appear to be

tangent are tangent.

º
º
An angle with the vertex ON the circle can look like this:

The angle measure of the vertex is half the measureof the intercepted arc.
vertex
on the
circle
Find the angle measures
120o
º
º
200o
The vertex of an angle can be INSIDE the circle
but NOT on the center
Center
not center
To find the angle,
add the arc of the angle
and the arc opposite that arc
add those arcs and divide by 2
40o
160o
160 + 40 =
200 ÷ 2 =
º
º
Determine the angle measures marked as "x" and "y".
x =              º
10o
6o
x
100o
y =             º
y
10o
If the vertex of the angle is OUTSIDE the circle
subtract the two arcs inside the angle
then divide by 2
115o
35o
x
x =           º
Find the angle measures
200o
60o
º
180o
70o
º
Solve for the 
missing arc measure.
260o
80º
º
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