Question

For the given angles cad and dae, what is the measure of each angle considering they are complementary?

A. cad = 3/2 x + 20, dae = 2x
B. cad = 2x, dae = 3/2 x + 20
C. cad = 2x + 20, dae = 3/2 x
D. cad = 3/2 x, dae = 2x + 20

Answer 1

The measure of the angles CAD and DAE, considering they are complementary, is cad = 15 and dae = 40.

Step-by-step explanation:

To find the measure of the angles CAD and DAE, we need to determine the relationship between them as complementary angles.

Complementary angles add up to 90 degrees. So, we have the equation:

cad + dae = 90

In the given options, the correct choice is option D: cad = 3/2 x and dae = 2x + 20. Substituting these values into the equation, we have:

(3/2)x + (2x + 20) = 90

Simplifying the equation gives:

5x + 40 = 90

5x = 50

x = 10

Substituting this value of x back into the expressions for cad and dae gives:

cad = 3/2(10) = 15

dae = 2(10) + 20 = 40

Therefore, the measure of the angles cad and dae, considering they are complementary, is cad = 15 and dae = 40.