Question

Given the figure below, find the values of x and z.

Answer 1

z = 109 degrees

x = 13

Explanation:

Step 1:

We can tell that this is a linear pair, and linear pairs are equal to 180. So, we'd add two angles to 180.

Once we find the value of x, we'd find the value of y since both are congruent as they are vertical angles.

Step 2:

12x - 85 + 109 = 180

Reduce by combining like terms.

12x + 24 = 180

12x = 156

x = 13

Step 3:

As mentioned above, since angle z is congruent to the vertical angle z, it would be 109 degrees.

Answer 2

z = 109°

The Vertical Angle Th. states that if two angles are vertical, then they're congruent.

12x - 85 + 109 = 180

The sum of both angles is equivalent to 180 because both angles are supplements

12x - 85 = 180 - 109

12x - 85 = 71

12x = 71 + 85

12x = 156

x = 156/12

x = 13

Good luck!