Question

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Answer 1

10a)
m(∡AOB)=m(∡DOC)=47°
m(∡AOD)=m(∡COB)=180°-47°=133°
verificare  47°+133°+47°+133°=360°

10b)
m(∡MON)+m(∡MOQ)=x+3x=4x=180°     x= 180°:4=45°
m(∡MON)=m(∡POQ)=45°
m(∡MOQ)=m(∡PON)=3×45°=135°
verificare  45°+135°+45°+135°=360°

10c)
m(∡CAB)+m(∡BAE)=x+x+120°=180°     x= (180°-120°):2=30°
m(∡CAB)=m(∡EAD)=30°
m(∡BAE)=m(∡DAC=30°×120°=150°
verificare  30°+150°+30°+150°=360°

11a)
m(∡AMB)=90°-30°=60°
m(∡AME)=90°
m(∡BMC)=m(∡EMD)=30°
m(∡DMC)=180°-30°=150°
verificare  30°+60°+90+30°+150°=360°

11b) 
m(∡QOP)=90°-70°=20°
m(∡PON)=90°
m(∡ROQ)=m(∡MON)=70°
m(∡ROM)=180°-70°=110°
verificare  70°+20°+90°+70°+110°=360°

11c)
m(∡UOT)+m(∡TOZ)+m(∡ZOY)=x+2x+3x=180°  6x=180°   x=30°
m(∡UOT)=30°
m(∡TOZ)=2×30°=60°
m(∡ZOY)=3×30°=90°
m(∡UOT)=m(∡XOY)=30°
m(∡UOX)=180°-30°=150°
verificare  30°+60°+90°+30°+150°=360°

11d)
m(∡BAC)+m(∡CAD)+m(∡DAE)=x+x+10+5x+30=7x+40=180°
7x=140°   x=20°
m(∡BAC)=20°
m(∡CAD)=20°+10°=30°
m(∡DAE)=5×20°+30°=130°
m(∡FAE)=x+x+10°=20°+20°+10°=50°
m(∡FAB)=180°-50=130°
verificare  20°+30°+130°+50°+130°=360°