Question

In the following diagram,

ℓ
∥
m
.



Solve for each of the variables w, x, y, and z. For each solution, explain, in complete sentences which special angles allowed you to create an equation in order to find a solution.

Answer 1

• x + 75 = 180, as these two angles form a straight angle.
• x = 180° - 75° = 105°

y and x are supplementary angles as p is transversal of l and m:

• y + x = 180°
• y = 180° - x = 180° - 105° = 75°

z is same as 86° as vertical angles:

• z = 86°

w and z are supplementary angles as g is transversal of l and m:

• w + z = 180°
• w = 180° - z = 180° - 86° = 94°