Answer: The correct option is
(C) x = 38 and y = 104.
Step-by-step explanation: We are given to find the values of the variables x and y from the figure.
We know that
if two angles make a linear pair, then the sum of their measures is 180°.
From the figure, we note that
the angles with measures y° and 76° makes a linear pair, so we have
[tex]y^\circ+76^\circ=180^\circ\\\\\Rightarrow y+76=180\\\\\Rightarrow y=180-76\\\\\Rightarrow y=104.[/tex]
Also, the angles with measures 2x° and y° makes a linear pair, so we have
[tex]2x^\circ+y^\circ=180^\circ\\\\\Rightarrow 2x+y=180\\\\\Rightarrow 2x=180-104\\\\\Rightarrow 2x=76\\\\\Rightarrow x=\dfrac{76}{2}\\\\\Rightarrow x=38.[/tex]
Thus, the required values the variables are x = 38 and y = 104.
Option (C) is CORRECT.
