x = 75 simplify
DESCRIPTION
1 2. x = ( 80 + 70 ) Substitute. 1 2. x = mDEF Inscribed Angle Theorem. 1 2. x = ( mDE + mEF ) Arc Addition Postulate. Because EFG is the intercepted arc of D , you need to find mFG in order to find mEFG. Inscribed Angles. LESSON 12-3. Additional Examples. - PowerPoint PPT PresentationTRANSCRIPT
GEOMETRYHELP
x = 75 Simplify.
x = mDEF Inscribed Angle Theorem 12
x = (mDE + mEF) Arc Addition Postulate12
Because EFG is the intercepted arc of D, you need to find mFG in order to find mEFG.
Find the values of x and y.
x = (80 + 70) Substitute.12
Inscribed AnglesLESSON 12-3
Additional Examples
GEOMETRYHELP
y = 95 Simplify.
y = (70 + 120) Substitute.12
y = (mEF + mFG) Arc Addition Postulate12
y = mEFG Inscribed Angle Theorem12
The arc measure of a circle is 360°, so mFG = 360 – 70 – 80 – 90 = 120.
(continued)
Quick Check
Inscribed AnglesLESSON 12-3
Additional Examples
GEOMETRYHELP
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.
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.
The sum of the measures of the three angles of the triangle inscribed in O is 180. .
Inscribed AnglesLESSON 12-3
Additional Examples
Quick Check
GEOMETRYHELP
m BRT = 27 Simplify.
mRT = mURT – mUR Arc Addition Postulate
m BRT = mRT The measure of an angle formed by a tangent and a chord is half the measure of the intercepted arc (Theorem 12-10).
12
RS and TU are diameters of A. RB is tangent to A at point R. Find m BRT and m TRS.
..
m BRT = (180 – 126) Substitute 180 for m and 126 for mUR.
12
Inscribed AnglesLESSON 12-3
Additional Examples
GEOMETRYHELP
90 = 27 + m TRS Substitute.
63 = m TRS Solve.
m BRS = m BRT + m TRS Angle Addition Postulate
m BRS = 90 A tangent is perpendicular to the radius of a circle at its point of tangency.
(continued)
Use the properties of tangents to find m TRS.
Inscribed AnglesLESSON 12-3
Additional Examples
Quick Check