Answer:
y = 120°
z = 32°
Step-by-step explanation:
For the sake of simplicity, I labeled one of the interior angles as m < 1 (Please see the attached screenshot). I did this because m < 1 and the exterior angle on the same side of the transversal have the same measure of m < 60°.
Therefore, m < 1 = m < 60°
Next, since m < 1 = 60°, then we can add its measure to < y°, which will sum up to 180° (given that they are supplementary angles).
We can establish the following formula to solve for < y°:
m < 1 + < y ° = 180°
Let's rearrange the formula to isolate < y°:
< y ° = 180° - m < 1
Substitute the value of m < 1 into the revised formula:
< y = 180°- 60°
< y = 120°
Now that we have the value for y°, we can find out what the value of z is by creating another formula:
< (5z - 100)° = 180° - y°
Substitute the value of y° into the formula:
5z - 100° = 180° - 120°
Combine like terms:
5z - 100° = 60°
Add 100° on both sides:
5z - 100° + 100° = 60° + 100°
5z = 160°
Divide both sides by 5:
[tex]\frac{5z}{5} = \frac{160}{5}[/tex]
< z = 32°
Double-check whether we derived the correct answers by plugging in the values of y° and z° into the following formula:
y° + (5z - 100)° = 180° (because they are supplementary angles)
120° + [5(32) - 100]° = 180°
120° + [5(32) - 100]° = 180°
120° + [160 - 100]° = 180°
120° + 60° = 180°
180° = 180° (True statement).
Therefore, the value of y = 120° and z = 32°.
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