Question

Cine ma ajuta are coroana ​

Answer 1

Rezolvare:

a) AOD, BOC- unghiuri opuse la varf deci sunt egale asa ca: AOD=48 grade

360-2 x 48=264 grade

AOC, DOB- unghiuri opuse la varf deci:

AOC=264:2=132 grade

DOB= 132 grade

b) procedam ca la exercitiul anterior: PON=MOQ, adica MOQ=125 grade 37'

(360-2 x 125 grade 37'):2= (360- 251 grade 14'):2= 108 grade 46':2=

=54 grade 23' deci: NOQ, POM= 54 grade 23'

c)EOF=180 grade, rezulta: GOD= 180-60-35=85 grade

GOH= 180 grade, rezulta: FOH= 180-85-35=60 grade

deci EOH= 180-60= 120 grade

d) NOP=180 grade dar NOP= POQ+ QON

NOP= 4x+x

180=5x => x= 36 grade => NOQ= 36 grade

POQ= 4x => POQ= 4 x 36= 144 grade

MOP, NOQ- opuse la varf => MOP= 36 grade

MON, POQ- opuse la varf => MON= 144 grade

e) DOE= 180 grade, dar DOE=2x + 5x-23

180=2x + 5x-23

7x=180+23

7x=203

x=29 => DOA= 2 x 29= 58 grade

COE, DOA- opuse la varf => COE= 58 grade

AOE= 5 x 29 - 23= 145-23= 122 grade

AOE, DOC- opuse la varf => DOC= 122 grade

f) AOE- unghi drept => AOE=90 grade

BOE=90 grade => DOB= 90-42= 48 grade

DOC=180 grade => 180=48+ BOC

BOC=180-48

BOC= 132 grade

AOC, DOB- opuse la varf => AOC=48 grade

g) OE- bisectoarea unghiului COA

daca EOA= 22 grade => COA=44 grade

COA, DOB- opuse la varf => DOB=44 grade

COD= 180 grade => AOD= 180-44=36 grade

AOD, COB- opuse la varf => COB= 36 grade

h)OR- bis unghiului MOQ

OS- bis unghiului QON

daca SON= x:3 => QOS= x:3

ROS= 90 grade => 90=x+54+x:3

x+x:3=90-54

putem sa scrie x:3 si ca fractie(x/3) asa ca amplificam cu 3 la x

3x+x /3 =36

4x/3=36

inmultim mezii cu extremii de unde rezulta: 4x=3 x 36

4x= 108

x=27 grade => ROQ = 27+54= 81 grade

ROQ=MOR => MOQ= 81 x 2 => MOQ=162 grade

SON= 27:3 => SON=9 grade

SON=QOS => QON= 18 grade

MOP, QON- opuse la varf => MOP= 18 grade

MOQ, PON- opuse la varf => PON= 162 grade

Sper ca te-am ajutat!