10-2 Measuring Angles and Arcs

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Presentation transcript:

10-2 Measuring Angles and Arcs You measured angles and identified congruent angles. Identify central angles, major arcs, minor arcs, and semicircles, and find their measures. Find arc lengths.

Central angles Central angles are angles whose vertices are at the center of the circle. Central angle p. 706

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

Arcs—parts of a circle Minor arc AB There are three kinds of arcs made by central angles: Major arcs: greater than 180° Named with 3 letters Minor arcs: less than 180° Named with 2 letters Semi-circles: exactly 180° one-half of a circle A C B D Major arc ADB A B C D

Measures in Degrees Complete circle measures 360°. The measure of any semicircle is 180°. (½ of a circle) 360° 180° C A B

p. 707

Measures Measure of a minor arc is equal to the measure of the central angle. Measure of the major arc is equal to 360° minus the measure of its minor arc. W Y 80° X Z W mXZY = 360°−mWX 80° Y X Z

Answer:

Answer:

Answer:

Definition Congruent arcs are arcs in the same circle (or congruent circles) that have the same measure. A Y 60° 60° B X

p. 707

mLPK = 0.21(360) Find 21% of 360. = 75.6 Simplify. Answer:

Sum of arcs in a circle is 360. Substitution Simplify. Simplify. Answer:

A. 124.3 B. 140.4 C. 155.6 D. 165.9

Find each arc measure in סּL Q L 54° 306° 180° mMN mMPN mPQN 54° P

10-2Assignment Page 710, 12-24