Answer:
[tex]x=21[/tex]
Step-by-step explanation:
We have been given an image of two parallel lines cut by a transversal. We are asked to find the measure of x.
We know that corresponding angles of two parallel lines are equal. We can see that angle BCA and angle DAF are corresponding angles.
Let us find measure of angle BCA using angle sum property.
[tex]54^{\circ}+105^{\circ}+m\angle BCA=180^{\circ}[/tex]
[tex]159^{\circ}+m\angle BCA=180^{\circ}[/tex]
[tex]159^{\circ}-159^{\circ}+m\angle BCA=180^{\circ}-159^{\circ}[/tex]
[tex]m\angle BCA=21^{\circ}[/tex]
Therefore, the value of x is 21 degrees.
