Answer:
[tex] x = 13^\circ [/tex]
Step-by-step explanation:
A right angle is an angle that measures [tex]90^\circ[/tex]. In geometric terms, it is a quarter of a full rotation.
In this case, two angles, [tex]55^\circ[/tex] and [tex]9 + 2x^\circ[/tex], are the angles of a right angle.
To be the angles of a right angle, they must add up to [tex]90^\circ[/tex].
So, we can write the equation:
[tex] 55^\circ + (9 + 2x)^\circ = 90^\circ [/tex]
Now, solve for [tex]x[/tex]:
[tex] 55^\circ + 9^\circ + 2x^\circ = 90^\circ [/tex]
[tex] 64^\circ + 2x^\circ = 90^\circ [/tex]
[tex] 2x^\circ = 90^\circ - 64^\circ [/tex]
[tex] 2x^\circ = 26^\circ [/tex]
[tex] x = \dfrac{26^\circ}{2} [/tex]
[tex] x = 13^\circ [/tex]
Therefore, the value of x is 13°.
