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=(1)/(2)(mRT+mSU)=(1)/(2)(80+40)=(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°