Transparency 10 4 5 Minute Check on Lesson

Transparency 10 -4 5 -Minute Check on Lesson 10 -3 The radius of ⊙R is 35, LM NO, LM = 45 and m. LM = 80. Find each measure. 1. m NO 80° 2. m NQ 40° 3. NO 45 4. NT 22. 5 5. RT 26. 81 6. Which congruence statement is true if RS and TU are congruent chords of ⊙V? Standardized Test Practice: A RS SU B RS TU C ST RU Click the mouse button or press the Space Bar to display the answers. D RS ST

Lesson 10 -4 Inscribed Angles

Objectives • Find measures of inscribed angles • Find measures of angles of inscribed polygons

Vocabulary • Inscribed Angle – an angle with its vertex on the circle and chords as its sides

Circles – Inscribed Angles y J Y° x Center X° es X° l g ½ n A °= ) e le Y b i g cr ure an s In eas tral M en - (c E K Measure Y° = ½ measure Arc KEF F

In and Find the measures of the numbered angles. First determine Arc Addition Theorem

Simplify. Subtract 168 from each side. Divide each side by 2. So, m

Answer:

In and measures of the numbered angles. Answer: Find the

ALGEBRA Triangles TVU and TSU are inscribed in with Find the measure of each numbered angle if and ∆UVT and ∆ UST are right triangles. Since they intercept congruent arcs, then m 1 = m 2. The third angles of the triangles must also be congruent, so m 2 = m 4.

Angle Sum Theorem Simplify. Subtract 105 from each side. Divide each side by 3. Use the value of x to find the measures of Given Answer:

ALGEBRA Triangles MNO and MPO are inscribed in with Find the measure of each numbered angle if and Answer:

Quadrilateral QRST is inscribed in Find and Draw a sketch of this situation. If and

To find we need to know first find Inscribed Angle Theorem Sum of angles in circle = 360 Subtract 174 from each side. Inscribed Angle Theorem Substitution Divide each side by 2.

To find we need to know but first we must Inscribed Angle Theorem Sum of angles in circle = 360 Subtract 204 from each side. Inscribed Angle Theorem Divide each side by 2. Answer:

Quadrilateral BCDE is inscribed in find and Answer: If and

Summary & Homework • Summary: – The measure of the inscribed angle is half the measure of its intercepted arc – The angles of inscribed polygons can be found by using arc measures • Homework: – pg 549 -550; 7, 9, 10, 15, 22 -25