Answer:
Part 7) Adjacent angles
m<SUR and m<RUN
m<TUP and m<PUQ
Part 8) Vertical acute angles
m<SUR and m<PUQ
m<RUN and m<TUP
Part 9) Supplementary angles
m<SUT and m<TUQ
m<SUR and m<QUR
Part 10) [tex]m<QUR=139\°[/tex]
Part 11) m<RUQ is greater than m< TUR
Part 12) [tex]x=21\°[/tex]
Part 13) [tex]m<KMH=96\°[/tex]
Step-by-step explanation:
Part 7) we know that
we know that
Two angles are Adjacent when they have a common side and a common vertex
In this problem
m<SUR and m<RUN ----> are adjacent angles
because have a common side UR and a common vertex U
m<TUP and m<PUQ ----> are adjacent angles
because have a common side UP and a common vertex U
Part 8) we know that
An angle is acute when is measure is less than [tex]90[/tex] degrees
Vertical Angles are the pair of congruent angles opposite each other when two lines cross
In this problem
[tex]m<SUR=m<PUQ=41\°[/tex] ------> by vertical angles
[tex]m<RUN=m<TUP=49\°[/tex] ------> by vertical angles
Part 9) we know that
Two angles are supplementary if its sum is equal to [tex]180[/tex] degrees
In this problem
[tex]m<SUT+m<TUQ=180\°[/tex] ------> by supplementary angles
[tex]m<SUR+m<QUR=180\°[/tex] ------> by supplementary angles
Part 10) Find m<QUR
we know that
[tex]m<SUR+m<QUR=180\°[/tex] ------> by supplementary angles
we have
[tex]m<SUR=41\°[/tex]
substitute
[tex]41\°+m<QUR=180\°[/tex]
[tex]m<QUR=180\°-41\°=139\°[/tex]
Part 11) which is greater m<TUR or m< RUQ
we know that
m<TUR=m<TUS+m<SUR
substitute the values
[tex]m<TUR=90\°+41\°=131\°[/tex]
[tex]m<RUQ=m<QUR=139\°[/tex] ----> see the procedure problem 10
therefore
m<RUQ is greater than m< TUR
Part 12) Find the measure angle x
[tex]4x=84\°[/tex] ------> by vertical angles
solve for x
[tex]x=84\°/4=21\°[/tex]
Part 13) m<KMH
we know that
[tex]m<KMH+84\°=180\°[/tex] -----> by supplementary angles
[tex]m<KMH=180\°-84\°=96\°[/tex]
