E=28°,又∵△ABC≌△BAE,∴∠ABC=∠BAE=28°,故答案为:28. 17.(3分)如图,已知AE是△ABC的边BC上的中线,若AB=8cm,△ACE的周长比△AEB的周长多2cm,则AC= 10 cm.【解答】解:∵AE是△ABC的边BC上的中线,∴CE=BE,又∵AE=AE,△ACE的周长比△AEB的周长多2cm,∴AC﹣AB=2cm,即AC﹣8=2cm,∴AC=10cm,故答案为:10; 18.(3分)若x+3y﹣3=0,则2x•8y= 8 .【解答】解:∵x+3y﹣3=0,∴x=3﹣3y,∴2x•8y=23﹣3y•23y=23=8.故答案是:8. 三、解答题(本大题共7小题,共46分)19.(9分)(1)计算:(15x3y+10x2y﹣5xy2)÷5xy(2)计算:(3x+y)(x+2y)﹣3x(x+2y)(3)先化简,再求值:(x+2)(x﹣2)﹣(x+1)2,其中x=.【解答】解:(1)(15x3y+10x2y﹣5xy2)÷5xy=3x2+2x﹣y;(2)(3x+y)(x+2y)﹣3x(x+2y)=3x2+6xy+xy+2y2﹣3x2﹣6xy=xy+2y2;(3)(x+2)(x﹣2)﹣(x+1)2=x2﹣4﹣x2﹣2x﹣1=﹣2x﹣5,当x=时,原式=﹣2×﹣5=﹣1﹣5=﹣6. 20.(6分)如图,点E,H,G,N在一条直线上,∠F=∠M,EH=GN,MH∥FG.求证:△EFG≌△NMH.【解答】证明:∵EH=GN,∴EG=NH,∵MH∥FG,∴∠EGF=∠NHM,∴在△EFG和△NMH中∴△EFG≌△NMH. 21.(6分)计算下列各式:(1)(2).【解答】解:(1)原式=•(﹣)•=﹣;(2)原式=﹣==﹣ 22.(6分)如图所示,在△ABC中,∠BAC的平分线AD交BC于点D,DE垂直平分AC,垂足为点E,∠BAD=29°,求∠B的度数.
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