Question

If AB is perpendicular to AC and AB is parallel to CD, angle CBD = 28° and angle BDE = 75°, then x and y are respectively:

a) x = 28°, y = 75°
b) x = 75°, y = 28°
c) x = 52°, y = 75°
d) x = 28°, y = 52°

Answer 1

In the given question, AB is perpendicular to AC and AB is parallel to CD. The values of x and y are respectively a) x = 28° and y = 75°.

Step-by-step explanation:

In the given question, we have AB perpendicular to AC and AB parallel to CD. We are given that angle CBD = 28° and angle BDE = 75°.

Since AB is perpendicular to AC, angle CBD + angle BDE must equal 90°. Therefore, x = 28°.

Since AB is parallel to CD, angle BDE must also equal angle ACD. Therefore, y = 75°.

So, the values of x and y are respectively x = 28° and y = 75°.