Answer:
[tex]x=11\°[/tex]
m∠N=[tex]59\°[/tex]
m∠O=[tex]121\°[/tex]
Step-by-step explanation:
we know that
In a parallelogram opposite angles and opposite sides are congruent and consecutive angles are supplementary
so
In this problem
m∠M=m∠O
m∠L=m∠N
m∠M+m∠N=[tex]180\°[/tex] -------> by supplementary angles
substitute the values and solve for x
[tex]11x+(6x-7)=180\°[/tex]
[tex]17x=(180+7)\°[/tex]
[tex]x=11\°[/tex]
so
Statements
case A) [tex]x=11\°[/tex]
The statement is true ------> see the procedure
case B) m∠L=[tex]22\°[/tex]
The statement is False
we know that
opposite angles are congruent
so
m∠L=m∠N
m∠L=[tex]6x-7=6(11)-7=59\°[/tex]
case C) m∠M=[tex]111\°[/tex]
The statement is False
we know that
m∠M=[tex]11x=11(11)=121\°[/tex]
case D) m∠N=[tex]59\°[/tex]
The statement is True
we know that
m∠N=[tex]6x-7=6(11)-7=59\°[/tex]
case E) m∠O=[tex]121\°[/tex]
The statement is True
we know that
opposite angles are congruent
so
m∠O=m∠M
m∠O=[tex]11x=11(11)=121\°[/tex]
