Question

Write the answer as an integer or decimal what is m

Answer 1

Given: The angles below shown in the figure

$\begin{gathered} m\angle VTU=91^0 \\ m\angle WTU=151^0 \end{gathered}$

To Determine: The value of the angle

$m\angle VUW$

Solution:

The sum of the angles at a point is 360 degrees. Therefore

$m\angle VTU+m\angle WTU+m\angle VTW=360^0$$\begin{gathered} 91^0+151^0+m\angle VTW=360^0 \\ 242^0+m\angle VTW=360^0 \\ m\angle VTW=360^0-242^0 \\ m\angle VTW=118^0 \end{gathered}$

Using circle theorem, angle at the center is equal to twice angle at the circumference

Therefore

$\begin{gathered} m\angle VTW=\text{angle at the center} \\ m\angle VUW=angle\text{ at the circumference} \\ 2\times m\angle VUW=m\angle VTW \end{gathered}$$\begin{gathered} 2\times m\angle VUW=118^0 \\ m\angle VUW=\frac{118^0}{2} \\ m\angle VUW=59^0 \end{gathered}$

Hence, m∠VUW = 59⁰