Question

Given that the measure of Angle DAC = 40 degrees and the measure of Angle ABC = 120 degrees, find the indicated measures for each question. Find the value of x and y.

Answer 1

x = 120°, y = 20°

Explanation:

Let's recall that the four interior angles in any rhombus must have a sum of 360 degrees. In addition, the opposite interior angles must be equivalent, and the adjacent angles have a sum of 180 degrees.

∠ ABC and ∠ ADC are opposite interior angles, so they must have equivalent measurements, therefore x = 120 degrees.

To find the value of y, we use this equation because the interior angles of the Δ ADC add up to 180:

y = 180 - 120 - 40

y = 180 - 160

y = 20 degrees ⇒ z = 40 degrees