Question

To find the measure of

Answer 1

Let us first get the value of z,

$(2z-3)^0+(5z-6)^0=180^0$$\begin{gathered} 2z-3^0+5z-6^0=180^0 \\ \text{collec like terms,} \\ 2z+5z-3^0-6^0=180^0 \end{gathered}$$\begin{gathered} 7z-9^0=180^0 \\ 7z=180^0+9^0 \\ 7z=189^0 \end{gathered}$$\begin{gathered} z=\frac{189^0}{7} \\ z=27^0 \end{gathered}$

Hence, the value of z is 27°.

Let us now solve for the measure of angle M,

$m\angle M=(5z-6)^0$$\begin{gathered} \text{where z=27}^0 \\ \text{substitute the value of z into the expression and find the angle M} \end{gathered}$$m\angle M=(5\times27-6)^0$$\begin{gathered} =135^0-6^0 \\ m\angle M=129^0 \end{gathered}$

Hence, the value of the measure of angle M is 129°.