Measuring Angles and Arcs LESSON 10–2

Lesson Menu Five-Minute Check (over Lesson 10–1) TEKS Then/Now New Vocabulary Key Concept: Sum of Central Angles Example 1: Find Measures of Central Angles Key Concept: Arcs and Arc Measure Example 2: Classify Arcs and Find Arc Measures Theorem 10.1 Example 3: Real-World Example: Find Arc Measures in Circle Graphs Postulate 10.1: Arc Addition Postulate Example 4: Use Arc Addition to Find Measures of Arcs Key Concept: Arc Length Example 5: Find Arc Length Example 6: Find Arc Length using Radian Measure

Over Lesson 10–1 5-Minute Check 1 Name a radius. A. B. C. D.

Over Lesson 10–1 5-Minute Check 2 Name a chord. A.LF B.MF C.OM D.NF ___

Over Lesson 10–1 5-Minute Check 3 Name a diameter. A.OM B.OL C.NF D.MF ___ ____ ___

Over Lesson 10–1 5-Minute Check 4 A.2 B.3 C.4 D.5 Refer to the figure. Find BC.

Over Lesson 10–1 5-Minute Check 5 A.9 B.11 C.13 D.15 Refer to the figure. Find DE.

Over Lesson 10–1 5-Minute Check 6 A.6.5 in. B.10.9 in. C.13 in. D.17 in. Find the length of the radius of the circle.

TEKS Targeted TEKS G.12(B) Apply the proportional relationship between the measure of an arc length of a circle and the circumference of the circle to solve problems. G.12(D) Describe radian measure of an angle as the ratio of the length of an arc intercepted by a central angle and the radius of the circle. Also addresses G.12(A). Mathematical Processes G.1(B) G.1(E)

Then/Now You measured angles and identified congruent angles. Identify central angles, major arcs, minor arcs, and semicircles, and find their measures. Find arc lengths.

Vocabulary central angle arc minor arc major arc semicircle congruent arcs adjacent arcs arc length radian measure

Concept

Example 1 Find Measures of Central Angles Find the value of x.

Example 1 Find Measures of Central Angles Substitution Simplify. Add 2 to each side. Divide each side by 26. The sum of the measures of Answer: x = 7

Example 1 A.9 B.10 C.11 D.65 Find the value of x.

Concept

Example 2 Classify Arcs and Find Arc Measures Answer:

Example 2 Classify Arcs and Find Arc Measures

Example 2 Classify Arcs and Find Arc Measures Answer:

Example 2 Classify Arcs and Find Arc Measures Answer:

Example 2 A. B. C. D.

Example 2 A. B. C. D.

Example 2 A. B. C. D.

Concept

Example 3 Find Arc Measures in Circle Graphs m  LPK= 0.21(360)Find 21% of 360. = 75.6Simplify. Answer:

Example 3 Find Arc Measures in Circle Graphs

Example 3 Find Arc Measures in Circle Graphs Sum of arcs in a circle is 360. Substitution Simplify. Answer:

Example 3 A B C D.165.9

Example 3 A B C D.201.4

Concept

Example 4 Use Arc Addition to Find Measures of Arcs.

Example 4 Use Arc Addition to Find Measures of Arcs Arc Addition Postulate Substitution= = 90 Answer:

Example 4 Use Arc Addition to Find Measures of Arcs

Example 4 Use Arc Addition to Find Measures of Arcs Arc Addition Postulate Substitution = = m  IMJ + m  JMK = 148 Answer:

Example 4 A.180 B.90 C.52 D.38

Example 4 A.52 B.90 C.142 D.180

Concept

Example 5 Find Arc Length Arc Length Equation Substitution Answer: Use a calculator. cm

Example 5 Find Arc Length Arc Length Equation Substitution Use a calculator.

Example 5 Find Arc Length Arc Length Equation Substitution Use a calculator. Answer:

Example 5 A.3.56 cm B.3.77 cm C.3.98 cm D.4.21 cm

Example 5 A cm B cm C cm D cm

Example 5 A cm B cm C cm D cm

Find Arc Length Using Radian Measure Answer:

A cm B cm C cm D cm P A B 15.1cm

Measuring Angles and Arcs LESSON 10–2