In a parallelogram the opposite angles are equal in measure, then, in our case:
[tex]6y+5=71[/tex]
Solving for y:
[tex]y=\frac{71-5}{6}[/tex][tex]y=\frac{66}{6}[/tex][tex]y=11[/tex]
Also, we have to consider that any two adjacent angles add up to 180°, meaning:
[tex](3x-8)+71=180[/tex][tex]3x-8+71=180[/tex][tex]3x+63=180[/tex][tex]x=\frac{180-63}{3}[/tex][tex]x=\frac{117}{3}[/tex][tex]x=39[/tex]
Using the same logic as the one used to calculate y, we can do the following:
[tex](6z+7)=(3x-8)[/tex]
However, as we know x = 39° we can solve for z:
[tex]6z+7=3\cdot(39)-8[/tex][tex]6z=117-8-7[/tex][tex]z=\frac{102}{6}[/tex][tex]z=17[/tex]
Answer:
• x = 39°
,
• y = 11°
,
• z = 17°
