Question

find the value of x,yand z

Answer 1

Hi there!

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At first give name to the line segments. [attachment]

Now, AOB is a straight line and OC stands on it.

∠AOC + ∠COB = 180° [Linear pair]

⇒2y + 30° = 180 °

⇒2y = 180 - 30

⇒2y = 150

⇒y = 150 / 2

⇒y = 75°

Again,

COD is a straight line and OB stands on it.

∠COB + ∠BOD = 180° [Linear pair]

⇒30 ° + 3x = 180

⇒3x = 180 - 30

⇒3x = 150

⇒x = 150 / 3

⇒x = 50°

Again,

AOB is a straight line and OD and OE stands on it.

∠BOD + ∠DOE + ∠EOA = 180° [Linear pair]

∠BOD = 3x
∠BOD = 3 × 50
∠BOD = 150°

Now,

∠BOD + ∠DOE + ∠EOA = 180°

⇒150 + 15 + z = 180

⇒165 + z = 180

⇒z = 180 - 165

⇒z = 15°

Hence,

x = 50°

y = 75°

z = 15°

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Thanks for the question!

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Answer 2

30° = z+ 25°

=>Z=30-25

Z=5°

2y+z+25= 180°(angles on a line sum up 180°)

2y+30= 180°

2y= 150°

y = 75°

3x=2y(vertically opposite angles)

3x=150°

=> x=150/3

=> x= 50°

Thank you