Answer:
x=12 y=6 m(ABC)=102 m(BCD)=78 m(DAB)=78
Step-by-step explanation:
alright mate so lets start with the properties of parallelogram:
- Opposite angles are equal
- Sum of any two adjacent angles is 180degree
(there are more but we will use those here)
- so lets start with 1st property for help:
m(BCD) is opposite angle for m(DAB) so those equations should be equal each other and this will give us a hint
[tex]6x+y=4x+5y\\2x=4y\\x=2y[/tex] i just changed the places of x to be in one place and s same for y then divided both sides by 2
- Now lets use the 2nd property (sum of two adjacent angles is 180)
m(ABC) is adjacent to m(BCD) so
[tex](7x+3y)+(4x+5y)=180[/tex] add x to x and y to y it will be
[tex]11x+8y=180\\[/tex]
- Now we going to use the first one x=2y in this equation so we can deal with one variable
replace x with 2y so 11x will be 22y
[tex]22y+8y=180\\30y=180\\y=6[/tex] added the y to y and then divided both sides by 30
[tex]x=2y \\x=2*6=12[/tex]
now we got x and y
then lets start to substitute every x and y in the equations
- [tex]7x+3y\\7*12+3*6=102\\[/tex]
- [tex]4x+5y\\4*12+5*6=78[/tex]
3.[tex]6x+y\\6*12+6=78[/tex]
now we got everthing hope i helped you sorry also for being late it toook alot to type it so you can understand
