Question

Lines AB and CD are straight lines. Find x and y. Give reasons to justify your solutions.

Answer 1

1) x = 14°, y = 5°

2) x = 18.5°, y = 37°

Step-by-step explanation:

1) ∠AOC and ∠BOD are vertical angles, then ∠BOD = 25°

∠MOD = ∠MOB + ∠BOD = 90°

3x + 23° + 25° = 90°

3x = 90° - 23° - 25°

x = 42°/3

x = 14°

∠LOB = ∠LOM + ∠MOB = 90°

5y + 3x + 23° = 90°

5y = 90° - 23° - 3(14°)

y = 25°/5

y = 5°

2) ∠AOC and ∠BOD are vertical angles, then ∠BOD = 16°

∠EOB = ∠EOD + ∠DOB = 90°

2y + 16° = 90°

y = (90° - 16°)/2

y = 37°

∠DOF = ∠BOF + ∠DOB = 90°

4x + 16° = 90°

x = (90° - 16°)/4

x = 18.5°