Answer:
x = 25° and y = 102°
Step-by-step explanation:
Given the transversal, line O, and that lines n || l :
m < (6x - 48)° and m < y° are vertically opposite angles, and are congruent.
To find the value of y, we can set up the following equation:
180° = 6x - 48° + 78°
180° = 6x - 30°
Subtract 30° on both sides oft the equation:
180°- 30° = 6x + 30° - 30°
150° = 6x
Divide both sides by 6 to solve for x:
[tex]\frac{150}{6} = \frac{6x}{6}[/tex]
25° = x
If you plug in the value of x in m < (6x - 48)°, you'll get:
m < (6x - 48)° = [6(25) - 48]° = 150° - 48 = 102°
Since m < (6x - 48)° = 102° and,
y° ≅ m < (6x - 48)°, then:
y° = 102°
The final answers are: x = 25° and y = 102°
You can verify whether this is correct by adding the values of m < (6x - 48)° and 78°, and you should get a sum of 180°.
