Question

Maths teacher draws a straight line AB shown on the blackboard as per the following figure.
(I)now he told Raju another line CD as in the figure.
(II) The teacher told to Ajay to mark ∠AOD as 2z.
(III)Suraj was told to Mark ∠AOD as 4y.
(IV)Clive made an angle ∠COE = 60°
(V)Peter marked ∠BOE and ∠BOD as y and X respectively​

Answer 1

Given : teacher draws a straight line AB

Raju to draw another line CD  intersecting AB

∠AOD = 2z

∠AOC = 4y

Drawn  ∠COE = 60°    between  C and B

∠BOE = y  , ∠BOD = x

To Find : value of x , y & z

Solution:

∠AOC +  ∠COE + ∠BOE  = 180°         ( linear pair) Straight line AB

4y + 60° +  y = 180°          

=> 5y = 120°  

=> y  = 24°

∠COE + ∠BOE + ∠DOB  = 180°         ( linear pair) Straight line CD

60° +  y  +x = 180°          

=>  60° +  24°  + x= 180°      

=>x   = 96°

or we could use a = 4y   ( vertically opposite angle)

Hence  x  = 4(24)  = 96°

x + 2z  = 180°   ( linear pair )

96° + 2z  = 180°

=> 2z  =84°

=> z = 42°

x = 96

y = 24

z = 42

x + 2z =  96 + 2(42)  = 180°

2(24) + 42 = 90

2y + z = 90°

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Answer 2

1) 96 2) 24 3) 48 4) 360 5) 2y+z= 90