Question

Use diagram to find the following 1. m angle RVS = 2. M angle TVU =

Answer 1

The pie chart provides the following information;

$\begin{gathered} m\angle RVS=(10x-10)^o \\ m\angle RVU=(8x-14)^o \\ m\angle UVT=8x^o \\ m\angle TVS=(5x+12)^o \end{gathered}$

The sum of angles in a circle is 360 degrees.

Thus, we have;

$\begin{gathered} (10x-10)^o+(8x-14)^o+8x^o+(5x+12)^o=360^o \\ 31x^o-12^o=360^o \\ 31x^o=360^o+12^o \\ 31x^o=372^o \\ x^o=\frac{372^o}{31} \\ x^o=12^o \end{gathered}$

Then;

(a)

$\begin{gathered} m\angle RVS=(10x-10)^o_{} \\ m\angle RVS=10(12)-10 \\ m\angle RVS=110^o \end{gathered}$

(b)

$\begin{gathered} m\angle TVU=8x^o \\ m\angle TVU=8(12) \\ m\angle TVU=96^o \end{gathered}$