9. x = 9 units
10.[tex]x^\circ = 12^\circ[/tex]
11.[tex]x^\circ = 6^\circ[/tex]
12.x =10 units
13. x= 1 unit
14. [tex]x =3^\circ[/tex]
15.[tex]x = 10^\circ[/tex]
16. [tex]x = 10^\circ[/tex]
Step-by-step explanation:
9.
Opposite sides of a parallelogram are equal to each other.
Therefore
2x-5 = 13
⇔2x = 13+5
⇔[tex]x = \frac{18}{2}[/tex]
⇔x = 9 units
10.
Sum of adjacent angles of parallelogram is [tex]180^\circ[/tex].
Therefore
[tex](11x-7)^\circ +55= 180 ^\circ[/tex]
⇔[tex]11x^\circ = 180 ^\circ -55^\circ +7^\circ[/tex]
⇔[tex]11x^\circ = 132^\circ[/tex]
⇔[tex]x^\circ=(\frac{132}{11} )^\circ[/tex]
⇔[tex]x^\circ = 12^\circ[/tex]
11.
Opposite angles of a parallelogram are congruent(equal).
Therefore
[tex]16x -4 = 92^\circ[/tex]
⇔ [tex]16x = 92^\circ +4[/tex]
⇔[tex]x^\circ =\frac{96 }{16}[/tex]
⇔[tex]x^\circ = 6^\circ[/tex]
12.
Opposite sides of a parallelogram are congruent.
Therefore
2x-11=9
⇔2x = 11+9
⇔2x=20
⇔[tex]x =\frac{20}{2}[/tex]
⇔x =10 units
13.
Opposite sides of a parallelogram are congruent (equal).
Therefore,
17x+1=18
⇔17x =18-1
⇔x= 1 unit
14.
Opposite angles of a parallelogram are congruent(equal).
Therefore,
[tex]12x -1 =35^\circ[/tex]
⇔[tex]12x =35^\circ +1^\circ[/tex]
⇔[tex]x= (\frac{36}{12} )^\circ[/tex]
⇔[tex]x =3^\circ[/tex]
15.
Sum of adjacent angles of parallelogram is [tex]180^\circ[/tex].
Therefore
[tex]10x +6 + 74^\circ=180^\circ[/tex]
⇔[tex]10x =180^\circ -74^\circ -6^\circ[/tex]
⇔[tex]x =( \frac{100}{10} )^\circ[/tex]
⇔[tex]x = 10^\circ[/tex]
16.
Opposite angles of a parallelogram are congruent(equal).
Therefore,
[tex]13x -10=120^\circ[/tex]
⇔[tex]13x = 120^\circ +10^\circ[/tex]
⇔[tex]x =( \frac{130}{13})^\circ[/tex]
⇔[tex]x = 10^\circ[/tex]
