Answer:
x = 105
z = 28
Step-by-step explanation:
Alternate exterior angles are exterior angles that do not have a common vertex on alternate sides of the transversal. Therefore, m < (3z - 9)° has the same measure as m < 75° because they are alternate exterior angles.
Also, the sum of m < (3z - 9)° and < x° = 180° because they are supplementary angles.
We can solve for the measure of < x° by:
x° = 180° - m < (3z - 9)°
x° = 180° - 75°
x° = 105°
Now that we have the value of x°, we can solve for the value of z by substituting the x° = 105° into the established equation:
m < (3z - 9)° + < x° = 180°
3z - 9 + 105° = 180°
3z + 96° = 180°
Subtract 96 from both sides:
3z + 96° - 96° = 180° - 96°
3z = 84°
Divide both sides by 3 to solve for z:
[tex]\frac{3z}{3} = \frac{84}{3}[/tex]
z = 28
Double-check whether our derived answers are correct:
m < (3z - 9)° + < x° = 180°
3(28) - 9 + 105° = 180°
3(28) - 9 + 105° = 180°
84° - 9° + 105° = 180
180° = 180° (True statement)
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