If two angles in the ration of 5:4 are represented by 5x and 4x, express each of the following statements as an equation; then find x and the angles.

Question

A. The angles are adjacent and together form an measuring 45 degrees

B. The angles are complementary

C. The angles are supplementary

D. The angles are two angles of a triangle whose third angle is their difference.

Answer 1

A. 5x + 4x = 90

9x = 90

x = 5

5x = 5(5) = 25°

4x = 4(5) = 20°

B. 5x + 4x = 90

9x = 90

x = 10

5x = 5(10) = 50°

4x = 4(10) = 40°

C. 5x + 4x = 180

9x = 180

x = 20

D. 5x - 4x = x, the 3rd angle

5x + 4x + x = 180

10x = 180

x = 18

5x = 5(18) = 90°

4x = 4(18) = 72°

Third angle - 5x - 4x = 90 - 72 = 18°

Check: 90 + 72 + 18 = 180°