Mathematics

Question

Find the measure of (Full question above)
Find the measure of 
 (Full question above)

2 Answer

  • Answer:

    ∠RUS = 90°

    Step-by-step 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°

  • Answer:

    [tex]\large\boxed{m\angle RUS=90^o}[/tex]

    Step-by-step 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]

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