Inscribed Angles LESSON 12-3 Additional Examples Find the values of x and y. 2 Inscribed Angle Theorem 2 Arc Addition Postulate 2 Substitute. x = mDEF x = (mDE + mEF) x.
Download ReportTranscript Inscribed Angles LESSON 12-3 Additional Examples Find the values of x and y. 2 Inscribed Angle Theorem 2 Arc Addition Postulate 2 Substitute. x = mDEF x = (mDE + mEF) x.
Inscribed Angles LESSON 12-3 Additional Examples
Find the values of
x
and
y
.
x
=
mDEF
2
x
1 = (
mDE
2 +
mEF
) Inscribed Angle Theorem Arc Addition Postulate
x
1 = ( 80 2 + 70 ) Substitute.
x
= 75 Simplify.
Because
EFG
is the intercepted arc of
D
, you need to find
mFG
in order to find
mEFG
.
HELP GEOMETRY
Inscribed Angles LESSON 12-3 Additional Examples (continued)
The arc measure of a circle is 360 °, so
mFG
= 360 – 70 – 80 – 90 = 120.
y
1 =
mEFG
2
y
1 = (
mEF
+
mFG
)
y
1 = ( 70 2 + 120 )
y
= 95 Inscribed Angle Theorem Arc Addition Postulate Substitute.
Simplify.
Quick Check HELP GEOMETRY
Inscribed Angles LESSON 12-3 Additional Examples
Find the values of
a
and
b
.
By Corollary 2 to the Inscribed Angle Theorem,
an angle inscribed in a semicircle is a right angle
, so
a
= 90.
The sum of the measures of the three angles of the triangle inscribed in
O
is 180. Therefore, the angle whose intercepted arc has measure
b
must have measure 180 – 90 – 32, or 58. Because the inscribed angle has
half
the measure of the intercepted arc, the intercepted arc has
twice
the measure of the inscribed angle, so
b
= 2(58) = 116.
HELP Quick Check GEOMETRY
Inscribed Angles LESSON 12-3 Additional Examples
RS
and
TU
are diameters of
A
.
RB
is tangent to
A
at point
R
. Find
m BRT
and
m TRS
.
m BRT
1 =
mRT
2 The measure of an angle formed by a tangent and a chord is half the measure of the intercepted arc (Theorem 12-10).
mRT
=
mURT
–
mUR
Arc Addition Postulate
m BRT
1 = (180 – 126) 2 Substitute 180 for
m
and 126 for
mUR
.
m BRT
= 27 Simplify.
HELP GEOMETRY
Inscribed Angles LESSON 12-3 Additional Examples (continued)
Use the properties of tangents to find
m TRS
.
m BRS
= 90 A tangent is perpendicular to the radius of a circle at its point of tangency.
m BRS
=
m BRT
+
m TRS
Angle Addition Postulate 90 = 27 +
m TRS
63 =
m TRS
Substitute.
Solve.
Quick Check HELP GEOMETRY