Answer:
x = 110
y = 70
w = 110
z = 89
Step-by-step explanation:
Let's look at each individual angle, and see how to solve them.
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Angle x: This angle is a supplementary angle to 70°. This means that the sum of their angles add up to 180° as they lie on a straight line.
Solving:
[tex]x^\circ~ + 70^\circ =180^\circ\\\\x^\circ = 110^\circ\\\\\boxed{x= 110}[/tex]
Therefore, [tex]x=110[/tex]
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Angle y: This angle is alternate interior to angle x. This means that the sum of their angles add up to 180°.
Solving:
[tex]x^\circ+y^\circ = 180^\circ~ (\text{plug in 110 degrees for x})\\110^\circ + y^\circ = 180^\circ\\\\y^\circ = 70^\circ\\\boxed{y=70}[/tex]
Therefore, [tex]y=70[/tex]
[tex]\hrulefill[/tex]
Angle w: This angle is alternate interior to angle y. This means that the sum of their angles add up to 180°.
Solving:
[tex]y^\circ+w^\circ = 180^\circ~ (\text{plug in 70 degrees for y})\\\\70^\circ + w^\circ = 180^\circ\\\\w^\circ = 110^\circ\\\\\boxed{w=110}[/tex]
Therefore, [tex]w=110[/tex]
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Angle z: This angle is a vertical angle to the angle 89°. This means that the two angles are congruent(equal).
Solving:
[tex]z^\circ = 89^\circ\\\\\boxed{z = 89}[/tex]
Therefore, [tex]z=89[/tex]
[tex]\hrulefill[/tex]
Hope this helps!
