1. Inscribed Angles
Inscribed Angle: its vertex is on the circle and its sides are chords.
The arc that is inside the angle is known as the intercepted arc.
Intercepted arc
Inscribed Angle
Measure of Inscribed Angle: A B D C
The measure of the inscribed angle is ½ of the measure of its intercepted arc.
mADB = ½ mAB

2. Inscribed Angle = ½ (intercepted arc)
Using the above formula, find the inscribed angle or the intercepted arc.
90° S R Q T M N P
100° Z Y X W
115°
Find mSTQ
Find mZWX
Find mNMP
NMP = ½ (100)
NMP = 50°
90 = ½ (STQ)
180° = STQ
115 = ½ (ZWX)
230° = ZWX

3. Theorem: If two inscribed angles of a circle intercept the same are, then the angles are congruent.
Then C  D C B D E F G H C
Inscribed Polygons
mD + mF =180°
mE + mG = 180°
A quadrilateral can be inscribed in a circle if and only if its opposite angles are supplementary.

4. Find the values of the variables:z y
120°
80° E F G D
80° + z = 180°
z = 100°
y + 120° = 180°
y = 60°
So… A = 80°
B = 60°
C = 100°
D = 120°
3y + 3x = 180°
3y = 180° – 3x
y = 60° – x 2y 3y 5x 3x A B C D
3y + 3x = 180°
2y + 5x = 180°
2(60 – x) + 5x = – 2x + 5x = 180 3x = 60 x = 20
y = 60 – x y = 60 – 20 y = 40