Question

In the given figurelines AB, CD and EFmeetat ‘O’. Find the values of x,y,z, u.
look at the picture below and answer the question

Answer 1

GivEn:

• AB, CD, EF is a line which meet at O
• ∠BOD = 90°
• ∠DOF = 50°
• ∠FOA = u°
• ∠AOC = z°
• ∠COE = y°
• ∠EOB = x°

To finD:

• Value of x,y,z,u

Solution:-

Finding angle FOA :

Here, AB is a line and we know that angle on a line is always 180°

∴ ∠ AOB = 180°

Now,

∠AOB = ∠BOD + ∠DOF+∠FOA

➢180° = 90° + 50° + u

➢180° = 140° + u

➢ u = 180° - 140°

➢ u = 40°

∴ ∠ u = 40°

━━━✿━━━

Finding angle AOC :

Here, CD is line and ∠COD is 180°

Now,

∠COD = ∠DOF + ∠FOA+∠AOC

➢ 180° = 50° + 40° + z

➢ 180° = 90° + z

➢ z = 180° - 90°

➢ z = 90°

∴ ∠z = 90°

━━━✿━━━

Finding angle EOB :

Here, EF is a line and ∠EOF = 180°

Now,

∠EOF = ∠EOB +∠BOD+∠DOF

➢180° = x + 90°+ 50°

➢180° = x + 140°

➢x = 180° - 140°

➢x = 40°

∴ ∠x = 40°

━━━✿━━━

Finding angle COE :

Here, AB is a line and ∠ AOB = 180°

Now,

∠AOB =∠AOC +∠COE + ∠EOB

➢180° = 90° + y + 40°

➢180° = 130° + y

➢y = 180° - 130°

➢y = 50°

∴ ∠y = 50°

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