Special Types of Angles
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- Angelica Montgomery
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1 Objectives: to determine measures of complementary, supplementary, and vertical angles to name or identify complementary, supplementary, adjacent, and vertical angles...to name, identify and/or determine measures of alternate interior, alternate exterior, and corresponding angles ssessment nchor: 8.C.1.1 Identify, use and/or describe properties of angles, triangles, quadrilaterals, circles, pyramids, cubes, prisms, spheres, cones, and/or cylinders. COMPLEMENTRY NGLES two angles whose measures add up to 90 SUPPLEMENTRY NGLES two angles whose measures add up to 180 BD and DC are complementary angles. ROT and SOT are supplementary angles. B D T C S O R GHF is complementary to GHF is supplementary to D E CHD is supplementary to EHD is complementary to C H G F
2 (Without a picture) Calculation nswer What is the complement of a 54 angle? = 36 What is the supplement of a 112 angle? = 68 What is the complement of a 19 angle? = What is the supplement of an 81 angle? What is the complement of a 37 angle? What is the supplement of an 18 angle? ***What is the complement of a 93 angle? ***What is the supplement of a 211 angle? ***If m = 28, m B = 48, and m C = 14 can we call these angles complementary angles? DJCENT NGLES two angles that share a vertex and a side, but no interior points VERTICL NGLES two angles formed by intersecting lines and are opposite each other **Vertical angles are congruent WY and XZ are vertical angles. W X WX and WY are adjacent angles. Y Z 1 and 3 are vertical angles. 2 and 3 are adjacent angles
3 IF m FTE = 41, then... C F m BTD = m CTF = D T E m TB = m TE = B m CTD = IF m 5 = 71, then... m 2 = m 4 = m 1 = m 6 = m 3 = Write an equation using BD and DBC. Then solve for x. D (3x 14) B (2x + 9) C m BD = m DBC = Write an equation using RS and TV. Then solve for x. R S (5x 18) T (4x + 7) V m RS = m SV =
4 TRNSVERSL a line that intersects two other lines at two different points CORRESPONDING NGLES non-adjacent angles that lie on the same side of the transversal and in corresponding positions LTERNTE INTERIOR NGLES angles that are on opposite sides of the transversal, and are between the two lines Transversal: a line that intersects two other lines in different points TERNTE EXTERIOR NGLES angles that are on opposite sides of the transversal, and are outside the two lines Corresponding angles: angles that lie on the same side of the transversal and in corresponding positions lternate Interior angles: angles that lie on opposite sides of the transversal and in the interior of the pair of lines *** When a transversal intersects two PRLLEL lines corresponding angles are congruent ND alternate interior angles are congruent ND alternate exterior angles are congruent!! Line p is a transversal. p m Pairs of corresponding angles: 1 n 1 and 5 2 and and 7 4 and Pairs of alternate interior angles: and 8 3 and 5 7 Pairs of alternate exterior angles: 1 and 7 4 and 6
5 IF m 4 = 114, then... Lines a and b are parallel. m 1 = m 6 = 1 2 m 2 = m 7 = 3 4 m 3 = m 8 = 5 6 m 5 = 7 8 c a b Lines m and n are parallel. 1 (7x + 35) Write an equation using 2 and 4. Then solve for x. 3 (3x 5) y m n m 7 = m 8 = Lines p and q are parallel. Write an equation using 2 and and 6. Then solve for x. p q 7 (5x 27) (3x + 31) 1 4 h m 7 = m 8 =
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