Question

2 lines intersect to form 4 angles. Clockwise, from top left, the angles are: x degrees, 105 degrees, z degrees, y degrees. Determine the measures of angles x, y, and z: x = ° y = ° z = °

Answer 1

The measures of angles x, y, and z are x = 105 degrees, y = 180 degrees, and z = 75 degrees.

Step-by-step explanation:

The sum of the angles formed by two intersecting lines is always equal to 360 degrees. In this case, the angles are given as x degrees, 105 degrees, z degrees, and y degrees. So, we can set up an equation:

x + 105 + z + y = 360

Since the angles are listed clockwise, we can assign values to each angle:

x = 105, y = z + 105, z = z

Substituting these values into the equation, we get:

105 + 105 + z + z = 360

210 + 2z = 360

2z = 150

z = 75

Therefore, x = 105 degrees, y = 75 + 105 = 180 degrees, and z = 75 degrees.