Answer:
x = 10
y = 71 degrees
Explanation:
Let's go ahead and find x as shown below;
[tex]\begin{gathered} 38+(7x+1)=(10x+9)\text{ (external angle is equal sum of opposite interior angles)} \\ 7x-10x=9-38-1 \\ -3x=-30 \\ x=\frac{-30}{-3} \\ \therefore x=10 \end{gathered}[/tex]
To find y, we need to know that;
[tex]\text{Angle}(7x+1)=7(10)+1=^{}71^{\circ}[/tex]
So let's call the third angle z. Let's go ahead and find z;
[tex]\begin{gathered} 38+71+z=180\text{ (sum of angles in a triangle)} \\ z=180-71-38 \\ \therefore z=71 \end{gathered}[/tex]
Therefore y = 71 degrees (vertically opposite angles and equal)
