10-4 Inscribed Angles You found measures of interior angles of polygons. Find measures of inscribed angles. Find measures of angles of inscribed polygons.

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Presentation transcript:

10-4 Inscribed Angles You found measures of interior angles of polygons. Find measures of inscribed angles. Find measures of angles of inscribed polygons.

Find the measure of each arc mDE mAED mEBD A B C D E 54° 54° 180° 306° What kind of angle is angle ECD? Central angle

Definition His name was inscribed on the award. The square is inscribed in the circle. A B C An inscribed angle is an angle with its vertex on a circle and sides that contain chords of the circle.

Intercepted Arc An intercepted arc has endpoints on the sides of an inscribed angle and lies in the interior of the inscribed angle Q S C R Intercepted arc PP P Center P is on a side of the inscribed angle Center P is inside the inscribed angle Center P is in the exterior of the inscribed angle

Sizing Up Inscribed Angles Measure the central angle What is the measure of the arc AB? Measure the inscribed angle Compare the measure of the central angle and the inscribed angle. A B C D

p. 723 The measure of an inscribed angle is half the measure of its intercepted arc. A B C

p. 724

Find the measure of each angle or arc indicated by a variable. 24° x°x° 160° y°y° C z°z° 48° 80° 90°

A. Find m  X. Answer: m  X = 43

B. = 2(52) or 104

A.47 B.54 C.94 D.188 A. Find m  C.

If two inscribed angles intercept the same arc, then they are congruent. A B C D p. 724

ALGEBRA Find m  R.  R   S  R and  S both intercept. m  R  m  SDefinition of congruent angles 12x – 13= 9x + 2Substitution x= 5Simplify. Answer: So, m  R = 12(5) – 13 or 47.

A.4 B.25 C.41 D.49 ALGEBRA Find m  I.

An inscribed angle that intercepts a semicircle is a right angle. p. 725

ALGEBRA Find m  B. ΔABC is a right triangle because  C inscribes a semicircle. m  A + m  B + m  C= 180 Angle Sum Theorem (x + 4) + (8x – 4) + 90 = 180Substitution 9x + 90= 180Simplify. 9x= 90Subtract 90 from each side. x= 10Divide each side by 9. Answer: So, m  B = 8(10) – 4 or 76.

10-4 Assignment Page 727, 11-18, 23-24