Question

If the measure if arc RT=80 degrees and the measure of arc US=40 degrees, what is the m<2?

Answer 1

We can start by finding the measure of 1, that is the supplememtary angle to 2.

The measure of <1 is equal to half the sum of the arcs RT and SU:

$m\angle1=\frac{1}{2}(mRT+mSU)=\frac{1}{2}(80+40)=\frac{120}{2}=60\degree$

As <2 is supplementary of <1, we have:

$\begin{gathered} m\angle2=180-m\angle1 \\ m\angle2=180-60 \\ m\angle2=120\degree \end{gathered}$

Answer: m<2 = 120°