Wht else cn you do? ngle sums The size of specil ngle types lernt erlier cn e used to find unknown ngles. tht form stright line dd to 180c. lculte the size of + M, if L is stright line M + L = 180c( stright ngle) 41c 73c L + LM + + + + M = + L = 180c ` 41c + 73c + + M = 180c ` + M = 180c - 41c - 73c + M = 66c tht re prt of full revolution re clled ngles t point nd they dd to 360c. lculte the size of + ere is right-ngle exmple. lculte the size of + + + + + + + = 360c ` 38c + 62c + 125c + + = 360c ` + = 360c - 38c - 62c - 125c + = 135c + K, + MK nd + LKM if they re ll the sme size K M L + K + + MK + + LKM = 90c ` + K, + MK nd + LKM = 90c ' 3 ` + K, + MK nd + LKM = 30c 62c 38c 125c The ngles joined t vertex sum to equl 360c + KL is right-ngle which equls 90c ' 3 s they re ll the sme size 26 10 SRIS TI 3 Lerning
Wht else cn you do? Your Turn ngle sums 1 For ech of these digrms, clculte the size of the missing ngle: K 13c 29c L M 17c 14c GL SUMS * GL SUMS * GL SUMS * +.../.../20... + K = + = c W X Y 72c 76c 203c Z d Smll dots cn e used to show equl sized ngles Q R V U T S + XY = ch ngle = 2 Verticlly opposite ngles cn e used to help find the unknown ngles for these. nd re stright lines 127c 83c K nd M re stright lines Q M 34c 88c 76c K + = + M = 3 Lerning SRIS 10 TI 27
Wht else cn you do? Your Turn ngle sums 3 Use the prllel line ngle properties to help find the size of these ngles: W 70c X G 47c U + W = 84c 130c V F I + G = + X = + GF = + X = + G = + W = + GF = omo Time! 4 Give these tricky ones go! You hve the skills now to use few different ngle properties for ech one. K nd Q re stright, prllel lines. nd re stright lines. 119c Q nd re stright, prllel lines. I 46c 141c K + Q = + FG = int: find F + F first G + Q = + Q = + FI = int: find + IF first 28 10 SRIS TI 3 Lerning
Wht else cn you do? ngle prolems Mny rel life prolems cn involve the ppliction of the ngle properties covered in this ooklet. This one uses the ngle sum of revolution. Trinity is lindfolded nd spun round in children s prty gme. If it tkes her 7 2 1 equl-sized steps to complete ech circle, how mny degrees does she turn with ech step? 1 complete circle = 1 revolution =360c ` umer of degrees turned with ech step = 360c ' 7 1 2 = 48c ` Trinity spins 48c with ech step she tkes. lwys nswer prolems with sttement ere is nother prolem. Five people were holding lengths of rope ll tied together t the centre. They need to move round until the ngle etween ech rope is the sme. xplin how ech person should move if Kim nd Rohn must oth sty still. Kim lculte the size ech ngle needs to e. Wei ` 360c ' 5 = 72c t point dd to 360c 92c 37c 100c 44c 87c Rohn Kim nd Rohn cnnot move. Wei moves 100c - 72c = 28c counter-clockwise Sung-Li ` ngle etween Kim nd Wei = 72c rin Sung-Li moves 92c - 72c = 20c clockwise ` ngle etween Kim nd Sung-Li = 72c Sung-Li's movements leve rin 20c + 37c = 57c wy from her. ` rin moves 72c - 57c = 15c counter-clockwise ` ngle etween Sung-Li nd rin 87c - 15c = 72c rin's movements tke her 15c closer to Rohn ` ngle etween rin nd Rohn = 87c - 15c = 72c ` ngle etween Wei nd Rohn = 72c nly ngle left over 3 Lerning SRIS 10 TI 29
Wht else cn you do? Your Turn ngle prolems 1 While performing circulr llet move, net turned the first hlf esily nd then with some extr effort, mde it 5 of the remining wy round. 6 ow mny degrees ws net wy from completing the full circle?.../.../20... GL RLMS * GL RLMS *?c Strt position Rememer me? She immeditely recovers nd strts her second move fcing where she hd stopped. If she successfully turns nother 180c in the sme direction, how mny degrees wy from the strt position is net now? 2 ert is uilding nother we, this time etween two stright, prllel ems ;; WX YZ. is we hs three stright supports:, nd G. W G X 28c 47c Y K Z ert wnts to put in nother stright support K tht psses through, strting t (etween W nd ) nd finishing t K (etween nd Z). rw in the support K tht mtches ert s wishes. Wht is the size of + if ll the cute ngles ginst the em WX re complementry? 30 10 SRIS TI 3 Lerning
Wht else cn you do? Your Turn ngle prolems 3 toy root is progrmmed to move to ll of the discs shown elow. It strts on disc fcing in the direction of the rrow. When it reches ech disc, the root remins fcing the direction it ws during the previous move. me the order of the discs it moves to if it follows these instructions in order: Turn right-ngle clockwise nd trvel forwrd to the next disc. omplete full revolution nd then trvel forwrd to the next disc. Turn counter-clockwise 200c nd trvel forwrd to the next disc. Turn clockwise 270c nd trvel forwrd to the next disc. Turn clockwise 80c then trvel in reverse (ckwrds) to the next disc. Turn counter-clockwise n cute ngle nd trvel forwrd to the lst disc. F G isc order: 4 s prt of tresure hunt, prticipnts must complete puzzles to receive the nme of the next destintion. t one stop, the puzzle is this: 27c Step 1: If + is stright ngle, clculte the complement of + nd dd it to one of the ngles formed when + is divided into nine equl sized prts. Step 2: lculte the size of reflex +, sutrct the vlue of step 1 from it nd then dd the supplement of + to the nswer. Wht nswer will win you the nme of the next destintion? 3 Lerning SRIS 10 TI 31