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Transcript 
10.4 – Use Inscribed Angles and
Polygons
Inscribed angle: An angle whose vertex is on
a circle and whose sides are
chords of the circle
Intercepted Arc: An arc that is inside an
inscribed angle
Inscribed Polygon : A polygon that has all of its
vertices on a circle
Circumscribed Circle: The circle that contains
the vertices of a polygon
half
The measures of an inscribed angle is ________
the measure of its ______________
arc.
intercepted
2x
x
D = AB
2
intercept
If two inscribed angles of a circle _____________
the same arc, then the angles are _____________.
congruent
D  C
A ________
right triangle is inscribed in a circle iff
the _______________
is a diameter of the circle.
hypotenuse
B is a right angle
because it inscribes a
semicircle.
quadrilateral
A ____________________
can be inscribed in a
circle iff its opposite angles are ______________.
supplementary
mD + mF = 180°
mE + mG = 180°
Find the indicated measure.
158
=
= 79°
2
Find the indicated measure.
180
=
= 90°
2
90°
180°
Find the indicated measure.
= 40  2 = 80°
Find the indicated measure.
92
=
= 46°
2
92°
88°
88°
Find the indicated measure.
80
=
= 40°
2
100°
80°
Find the indicated measure.
56
=
= 28°
2
56°
Find the measure of A and C.
80
mA =
= 40°
2
64°
80°
64
mC =
= 32°
2
Find the measure of A and C.
146°
146
mA =
= 73°
2
62
mC =
= 31°
2
62°
68
mPNO = 2 = 34°
62
mQNP = 2 = 31°
62°
= 62°
62°
= 130°
62°
= 112°
112°
62°
= 248°
112°
62°
Decide whether a circle can be circumscribed
about the figure.
No,
70 + 130  180
Decide whether a circle can be circumscribed
about the figure.
No,
92 + 89  180
Decide whether a circle can be circumscribed
about the figure.
No,
115 + 63  180
Find the value of the variables.
5x + 110 = 180
5x = 70
x = 14°
2y + 104 = 180
2y = 76
y = 38°
Find the value of the variables.
x + 108 = 180
y + y = 180
x = 72°
2y = 180
y = 90°
Find the value of the variables.
44°
4x = 84+44
2
8x = 128
x = 16°
7y = 152+44
2
14y = 196
y = 14°
Find the value of the variables.
171°
12x = 96+48
2
24x = 144
3y = 48+171
2
6y = 219
x = 6°
y = 36.5°
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