Find the measure of (Full question above)
Question
2 Answer

1. User Answers 19allenethm
Answer:
∠RUS = 90°
Stepbystep explanation:
PT is a line. This means that it has a measure of 180°
This means that all of the angles that it is broken up into must add together to equal 180°.
In this case, ∠PUQ +∠QUR +∠RUS +∠SUT = 180°
As we have the measures for all of the angles aside from ∠RUS, we can solve for that
First, let us input each of the measures of the angles
39+23+∠RUS+28=180
Now all we need to do is isolate ∠RUS by subtracting everything to the other side
Once that is done, we get
∠RUS = 90°

2. User Answers gmany
Answer:
[tex]\large\boxed{m\angle RUS=90^o}[/tex]
Stepbystep explanation:
[tex]m\angle PUT=m\angle PUQ+m\angle QUR+m\angle RUS+m\angle SUT\\\\\text{We have:}\\\\m\angle PUT=180^o,\ m\angle PUQ=39^o,\ m\angle QUR=23^o,\ m\angle SUT=28^o\\\\\text{Substitute:}\\\\180^o=39^o+23^o+m\angle RUS+28^o\\\\180^o=90^o+m\angle RUS\qquad\text{subtract}\ 90^o\ \text{from both sides}\\\\90^o=m\angle RUS[/tex]