We know that the arc cut off by a tangent has measure equal to twice the angle it cuts off. So, [tex]x = 2 \cdot 82 = \boxed{164}[/tex].
The sum of two angles that together occupy a straight line is [tex]180[/tex], so [tex]z+82 = 180[/tex], so [tex]z = 98[/tex]. Then, by the same fact we used above, [tex]y = 2 \cdot z = 2 \cdot 98 = \boxed{196}[/tex].
Feel free to post a comment if you have any questions!
