Answer:
Part 9) [tex]x=12[/tex]
Part 10) [tex]x=12\°[/tex]
Part 11) [tex]x=10\°[/tex]
Part 12) [tex]x=11\°[/tex]
Part 13)
a) [tex]SU=4\ units[/tex]
b) m∠VWX=[tex]40\°[/tex]
c) m∠WVX=[tex]50\°[/tex]
d) m∠XTV=[tex]60\°[/tex]
e) m∠XVT=[tex]30\°[/tex]
Step-by-step explanation:
Part 9) we have that
[tex]12=2x-12[/tex] ----->by SSA
solve for x
[tex]2x=24[/tex]
[tex]x=12[/tex]
Part 10)
In the isosceles triangle of the left the vertex angle is equal to
[tex]180\°-68\°*2=44\°[/tex]
Find the measure of angle 2
m∠2=[tex]90\°-44\°=46\°[/tex]
m∠2=[tex]4x-2[/tex]
[tex]4x-2=46\°[/tex]
solve for x
[tex]4x=48\°[/tex]
[tex]x=12\°[/tex]
Part 11)
Find the base angle in the isosceles triangle of the top
[tex]180\°-118\°=62\°[/tex]
Find the vertex angle in the isosceles triangle of the top
[tex]180\°-2*62\°=56\°[/tex]
Find the vertex angle 2 in the isosceles triangle of the bottom
[tex]180\°-56\°=124\°[/tex] ------> this is the measure of angle 2
m∠2=[tex]124\°[/tex]
m∠2=[tex]12x+4[/tex]
[tex]12x+4=124\°[/tex]
[tex]12x=120\°[/tex]
[tex]x=10\°[/tex]
Part 12)
m∠2=[tex]146\°[/tex] ------> by corresponding angles
m∠2=[tex]13x+3[/tex]
[tex]13x+3=146\°[/tex]
[tex]13x=143\°[/tex]
[tex]x=11\°[/tex]
Part 13)
a) we have that
SU=UW ------> given problem
[tex]3x+1=x+3[/tex]
[tex]2x=2[/tex]
[tex]x=1[/tex]
therefore
[tex]SU=3x+1=3+1=4[/tex]
[tex]SU=4\ units[/tex]
b) we know that
m∠VWX=[tex]4y\°[/tex]
in the right triangle UVW find the value of y
The sum of the internal angles of a triangle is equal to [tex]180\°[/tex]
so
[tex]180\°=4y+90\°+50\°[/tex]
[tex]180\°=4y+140\°[/tex]
[tex]4y=40\°[/tex]
[tex]y=10\°[/tex]
so
m∠VWX=[tex]4y\°=40\°[/tex]
Part c) we know that
in the right triangle VWX
The sum of the internal angles of a triangle is equal to [tex]180\°[/tex]
so
m∠WVX=[tex]180\°-(4y+90\°)[/tex]
m∠WVX=[tex]180\°-(40\°+90\°)[/tex]
m∠WVX=[tex]50\°[/tex]
Part d) we know that
in the right triangle XTV
The sum of the internal angles of a triangle is equal to [tex]180\°[/tex]
so
m∠XTV=[tex]180\°-(40\°-y+90\°)[/tex]
m∠XTV=[tex]180\°-(40\°-10\°+90\°)[/tex]
m∠XTV=[tex]60\°[/tex]
Part e) we know that
m∠XVT=[tex](40\°-y)[/tex]
substitute the value of y
m∠XVT=[tex](40\°-10\°)[/tex]
m∠XVT=[tex]30\°[/tex]
