Question

Case Study
5. Read the source/text given below and answer any four questions (1x4 - 4)
Maths teacher draws a straight line AB shown on the black board as per following
figure


(). Now he told Raju to draw another line CD as in the figure.
(il). The teacher told Ajay to mark angleAOD as 2z.
(ili). Suraj was told to mark angle AOC as 4y.
(iv). Clive made an angle angleCOE =60°
(v). Peter marked angle B0E and angleBOD as y and x respectively.
Now answer the following questions
(1). What is the value of y?
(a). 48°
(b).24°
(c)96°
(D)120°
(ii). What is the value of x?
(a). 48°
(b), 96°
(c). 100°
(D)120°
(iii). What is the value of z?
(a). 48°
(b). 96°
(c). 42°
(D)120°
(iv). What should be the value of x + 2z?
(a). 148°
(b). 360°
(c): 180°
(d). 120°
​

Answer 1

Given: ∠AOD = 2z, ∠AOC = 4y, ∠COE =60°, ∠BOE = y and ∠BOD = x

To Find: (1) What is the value of y ?

              (2) What is the value of x ?

              (3) What is the value of z ?

              (4) What should be the value of x + 2z ?

Step-by-step explanation:

Diagram of question is attached below

∠AOC = ∠BOD ( vertically opposite angles)

4y = x ------ (i)

∠BOD + ∠BOE + ∠COE = 180°

x + y + 60° = 180°

Putting the value of 'x' from equation (i)

4y + y + 60° = 180°

5y + 60° = 180°

5y = 180° - 60°  ( keeping variable on left side and taking constant value on other side and changing the operational sign )

5y = 120°

$y = \frac{120}{5}$

y = 24° -----(ii)

putting value of 'y' in equation (i)

$4\times y =x\\4\times 24 = x\\96 = x$

x = 96°

∠AOD = ∠BOC (vertically opposite angles)

2z = 60° + y

putting the value of 'y' from equation (ii)

2z = 60° + 24°

2z = 84°

$z =\frac{84}{2}$

z = 42°

(1) Value of x = 96°

(2) Value of y = 24°

(3) Value of z = 42°

(4) Value of 2z + x = 180° (as it is  making complete angle of AB line)

Answer 2

Answer:

(1) Value of x = 96°

(2) Value of y = 24°

(3) Value of z = 42°

(4) Value of 2z + x = 180° (as it is making complete angle of AB )