Question

Find the measure of arc URT

Answer 1

Hello!

This question is about relating vertical angles and their arc lengths.

Vertical angles have equal angle measures, meaning that they will also have the same arc measure.

We know that arc QR and arc UT have equal angle measures because they are formed with vertical angles.

That means since we know the measure of the other two arcs, which will both be 125 since they are formed with vertical angles, we can solve for the two unknown arc lengths.

A circle is 360 degrees, meaning that we can make the following equation,

`360=QR+UT+125+125`

`QR+UT+250=360`

`QR+UT=110`

Since QR = UT

`QR/UT=55`

Now, we can solve for arc URT using all the arc measures we have.

`URT=125+55+125`

`URT=305`

Hope this helps!