Concept. Example 1 Use Inscribed Angles to Find Measures A. Find m X. Answer: m X = 43.

Use Inscribed Angles to Find Measures

A. Find mX.

Answer: mX = 43

Use Inscribed Angles to Find Measures

B.

= 2(52) or 104

Use Inscribed Angles to Find Measures

ALGEBRA Find mR.

R S R and S both intercept . mR mS Definition of congruent angles

12x – 13 = 9x + 2 Substitutionx = 5 Simplify.

Answer: So, mR = 12(5) – 13 or 47.

Find Angle Measures in Inscribed Triangles

ALGEBRA Find mB.

ΔABC is a right triangle because C inscribes a semicircle.

mA + mB + mC = 180 Angle Sum Theorem(x + 4) + (8x – 4) + 90 = 180 Substitution

9x + 90 = 180 Simplify.9x = 90 Subtract 90 from each

side.x = 10 Divide each side by 9.

Answer: So, mB = 8(10) – 4 or 76.

Find Angle Measures

INSIGNIAS An insignia is an emblem that signifies rank, achievement, membership, and so on. The insignia shown is a quadrilateral inscribed in a circle. Find mS and mT.

Find Angle Measures

Since TSUV is inscribed in a circle, opposite angles are supplementary.

mS + mV = 180 mU + mT = 180 mS + 90 = 180 (14x) + (8x + 4) = 180

mS = 90 22x + 4 = 18022x = 176

x = 8Answer: So, mS = 90 and mT = 8(8) + 4 or 68.