1. Obj. 8 Angles Objectives: The student will be able to (I can): Correctly name an angle Classify angles as acute, right, or obtuse IdentifyIdentify linear pairs vertical angles complementary angles supplementary angles and set up and solve equations. Obj. 8 Angles The student will be able to (I can): Classify angles as acute, right, or obtuse and set up and solve equations.

2. angle vertex A figure formed by two rays or sides with a common endpoint. Example: The common endpoint of two rays or sides (plural vertices(plural vertices Example: A is the vertex of the above angle A figure formed by two rays or sides with a common endpoint. The common endpoint of two rays or sides vertices). A C R vertices). Example: A is the vertex of the above angle 3. Notation: An angle is named one of three different ways: 1. By the vertex and a point on each ray1. By the vertex and a point on each ray (vertex must be in the middle) : 2. By its vertex (if only one angle): 3. By a number: Notation: An angle is named one of three different ways: 1. By the vertex and a point on each ray E T A 1 1. By the vertex and a point on each ray (vertex must be in the middle) : TEA or AET By its vertex (if only one angle): E 3. By a number: 1 4. Example Which name is below? TRSTRS SRT RST 2 R Which name is notnotnotnot correct for the angle S R T 2 5. Example Which name is below? TRSTRS SRT RST 2 R Which name is notnotnotnot correct for the angle S R T 2 6. acute angle right angle Angle whose measure is greater than 0 and less than 90. Angle whose measure is exactly 90. obtuse angle Angle whose measure is greater than 90 and less than 180. Angle whose measure is greater than 0 and less than 90. Angle whose measure is exactly 90. Angle whose measure is greater than 90 and less than 180. 7. congruent angles Angles that have the same measure. mWIN = m WIN LHS N Notation: Arc marks indicate congruent angles. Notation: To write the measure of an angle, put a lowercase m in front of the angle bracket. mWIN is read measure of angle WIN Angles that have the same measure. LHS LHS L H S W IN Notation: Arc marks indicate congruent Notation: To write the measure of an angle, put a lowercase m in front of the angle WIN is read measure of angle WIN 8. interior of an angle Angle Addition Postulate The set of all points between the sides of an angle If D is in the interiorinteriorinteriorinterior mABD + m (part + part = whole) Example: If m m A The set of all points between the sides of interiorinteriorinteriorinterior of ABC, then ABD + mDBC = mABC (part + part = whole) Example: If mABD=50 and ABC=110, then mDBC=60 B D C 9. Example The mPAH = 125. P (2x+8) PAH = 125. Solve for x. A T H (3x+7) (2x+8) 10. Example The mPAH = 125. mPAT + m P (2x+8) mPAT + m PAH = 125. Solve for x. TAH = mPAH A T H (3x+7) (2x+8) TAH = mPAH 11. Example The mPAH = 125. mPAT + m P (2x+8) mPAT + m 2x + 8 + 3x + 7 = 125 PAH = 125. Solve for x. TAH = mPAH A T H (3x+7) (2x+8) TAH = mPAH 2x + 8 + 3x + 7 = 125 12. Example The mPAH = 125. mPAT + m P (2x+8) mPAT + m 2x + 8 + 3x + 7 = 125 5x + 15 = 125 PAH = 125. Solve for x. TAH = mPAH A T H (3x+7) (2x+8) TAH = mPAH 2x + 8 + 3x + 7 = 125 5x + 15 = 125 13. Example The mPAH = 125. mPAT + m P (2x+8) mPAT + m 2x + 8 + 3x + 7 = 125 5x + 15 = 125 PAH = 125. Solve for x. TAH = mPAH A T H (3x+7) (2x+8) TAH = mPAH 2x + 8 + 3x + 7 = 125 5x + 15 = 125 5x = 110 14. Example The mPAH = 125. mPAT + m P (2x+8) mPAT + m 2x + 8 + 3x + 7 = 125 5x + 15 = 125 PAH = 125. Solve for x. TAH = mPAH A T H (3x+7) (2x+8) TAH = mPAH 2x + 8 + 3x + 7 = 125 5x + 15 = 125 5x = 110 x = 22 15. angle bisector A ray that divides an angle into two congruent angles. Example: UY bisects SUN; thusUY bisects SUN; thus A ray that divides an angle into two congruent angles. SUN; thus SUY YUN S U N Y SUN; thus SUY YUN or mSUY = mYUN 16. adjacent angles Two angles in the same plane with a common vertex and a common side, but no common interior points. Example: 1 and 2 are adjacent angles. linear pair 1 and 2 are adjacent angles. Two adjacent angles whose noncommon sides are opposite rays. (They form a line.) Example: Two angles in the same plane with a common vertex and a common side, but no common interior points. 2 are adjacent angles. 1 2 2 are adjacent angles. Two adjacent angles whose noncommon sides are opposite rays. (They form a line.) 17. vertical angles Two nonadjacent angles formed by two intersecting lines. congruent.congruent.congruent.congruent. Example: 1 and 2 and Two nonadjacent angles formed by two intersecting lines. They are alwaysThey are alwaysThey are alwaysThey are always 1 2 3 4 1 and 4 are vertical angles 2 and 3 are vertical angles 18. complementary angles supplementary angles Two angles whose measures have the sum of 90. Two angles whose measures have the sum of 180. A and B are complementary. (55+35) A and C are supplementary. (55+125) Two angles whose measures have the sum Two angles whose measures have the sum 55 35 B are complementary. (55+35) C are supplementary. (55+125) A B C 125 19. Practice 1. What is m 2. What is m 3. What is m What is m1? What is m2? 1 60 What is m3? 51 2 105 3 20. Practice 1. What is m 180 60 = 120 2. What is m 3. What is m What is m1? 60 = 120 What is m2? 1 60 What is m3? 51 2 105 3 21. Practice 1. What is m 180 60 = 120 2. What is m 90 51 = 39 3. What is m What is m1? 60 = 120 What is m2? 51 = 39 1 60 What is m3? 51 2 105 3 22. Practice 1. What is m 180 60 = 120 2. What is m 90 51 = 39 3. What is m 105 What is m1? 60 = 120 What is m2? 51 = 39 1 60 What is m3? 51 2 105 3