Angles at a point add up to [tex]360^o[/tex]. The measure of [tex]m\angle ROS[/tex] is [tex]225^o[/tex]
Given that:
[tex]m\angle QOS = 46^o[/tex]
[tex]m\angle POR = 61^o[/tex]
[tex]m\angle POQ = 28^o[/tex]
The 4 angles (i.e. QOS, POR, POQ and ROS) are all angles at a point (i.e. point O).
This means that we can apply the angle at a point theorem.
The theorem is represented as:
[tex]m\angle QOS +m\angle POR +m\angle POQ + m\angle ROS = 360^o[/tex] --- i.e. angles at a point add up to [tex]360^o[/tex]
So, we have:
[tex]46^o + 61^o + 28^o + m\angle ROS = 360^o[/tex]
[tex]135^o + m\angle ROS = 360^o[/tex]
Collect like terms
[tex]m\angle ROS = 360^o -135^o[/tex]
[tex]m\angle ROS = 225^o[/tex]
Hence, the measure of [tex]m\angle ROS[/tex] is [tex]225^o[/tex]
Learn more about angles at:
https://brainly.com/question/15767203
