Question

diagrams are not drawn to scale. do numbers 10 and 12. i only care about the answers & the steps to get the answers. pls don’t take forever..

Answer 1

10. from the question; the circle theorem obeyed is "angled formed by semi-circle"

The angle formed in a semicircle is 90 degrees, hence

`m\angle XYZ=90^(\circ)`

This gives

`m\angle YXZ\text{ + m}\angle YZX\text{ = 90}`

But

`\begin{gathered} m\angle YXZ\text{ = 2x + 8} \\ m\angle YZX\text{ = 5X - 2} \end{gathered}`

Substituting values we get

`\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{ = }(84)/(7) \\ x\text{ = 12} \end{gathered}`

hence, x =12