Question

In the figure , AB is a straight line. Find the value of x and also find ∠AOC, ∠COD, ∠BOD?
AOC = 3x+17 cod = 2x-9 and bod = x

Answer 1

Given :

• AB is a straight line
• ∠AOC = (3x+17)°
• ∠COD = (2x-9)°
• ∠BOD = (x)°

To find :

• Measure of x° and each angle

Solution :

• ∠AOC + ∠COD + ∠BOD = 180°  (Linear Pair)
• 3x + 17 + 2x - 9 + x = 180°
• 6x + 8 = 180°
• 6x = 180 - 8
• 6x = 172°
•  x = ¹⁷²⁄₆
•  x = ⁸⁶⁄₃

★ The value of x° - ⁸⁶⁄₃°

★ Measure of each angle :

• ∠AOC = 3x + 17
• ∠AOC = 3 × ⁸⁶⁄₃ + 17
• ∠AOC = 103°
• ∠COD = 2x - 9
• ∠COD = 2 × ⁸⁶⁄₃ - 9
• ∠COD = 48.33°
• ∠BOD = x
• ∠BOD = ⁸⁶⁄₃
• ∠BOD = 28.66°

✯ ∠AOD = 103°

✯ ∠COD = 48.33°

✯ ∠BOD = 28.66°

✮ Their sum should be 180° (Angle sum property)

✮ 103+48.33+28.66 = 179.99° (Approx 180°)