10. from the question; the circle theorem obeyed is "angled formed by semi-circle"
The angle formed in a semicircle is 90 degrees, hence
[tex]m\angle XYZ=90^{\circ}[/tex]
This gives
[tex]m\angle YXZ\text{ + m}\angle YZX\text{ = 90}[/tex]
But
[tex]\begin{gathered} m\angle YXZ\text{ = 2x + 8} \\ m\angle YZX\text{ = 5X - 2} \end{gathered}[/tex]
Substituting values we get
[tex]\begin{gathered} 2x\text{ + 8 + 5x - 2 = 90} \\ 2x\text{ + 5x + 8 - 2 = 90} \\ 7x\text{ + 6 = 90} \\ 7x\text{ = 90 -6} \\ 7x\text{ = 84} \\ \text{divide both sides by 7} \\ x\text{ = }\frac{84}{7} \\ x\text{ = 12} \end{gathered}[/tex]
hence, x =12
