Victory for the ACT Exam 16e TG Sample

U NIT 4 | G EOMETRY • 505

STUDENT TEXT, p. 184 4. In the �igure below, x = ? F. G. 4 3 5 0 H. 60 J. 75

EXPLANATIONS

4. (H) Mathematics/Geometry/Lines and Angles CC: 8.G.A.5 CCRS: AVG.G.2 Difficulty Level = 1; Teaching Time = 5–8 minutes; Purpose = Example If y u n l°a bi setl he de ma negal seui rnet oh fe tthrei atnhgi rl ed, a n d then y 60 = , since it forms a linear, sa un pg lpel eomu tesni dt aer tyhpe atirri awnigt hl e t. hTeh u1 s2, 0 ° x y x 60 180 60 60 & & 180 x x 120 180 60 & . Aa nl tgelrenoaft iav et rl yi a, nr egml e ei ms ebqeur at lhtaot tahney seuxmt e r i o r of the two remote interior angles. Thus, 60 120 60 x x & .

Teaching Tip Ihf oswt u tdoe cnat lsc fuol ragt ee t ti nh tee sr ui omr aonf gt hl ees o f athpeomlyhgoown, tsohodwerive iatnt he ex amms epllvee. sFours i n g i( n3 s st iadnecse), ha at sr i 1a 8n 0g l° e. A( 4 ssqi ud ae rs e) /hraesc t3a6n0g°l ,e oc ar n1 s8e0e° (t2h)a. tS1t u8d0e° n t s (gne n- e2r)a il si ztahtei ocno. r r e c t

INTERIOR ANGLES OF ARBITRARY POLYGONS The sum, in degrees, of the interior angles of an n -sided polygon is ( ) n 180 2 − . Example: The �igure below has six sides, so the sum, in degrees, of the six angles is ( ) n 180 2 ( ) ( ) 180 6 2 180 4 720 . Notice that instead of memorizing the formula for the number of degrees in a polygon, you can reason that the polygon in the above �igure is composed of four non-overlapping triangles, and the number of degrees in each triangle is 180: 4(180) = 720.

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