Question

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Answer 1

Answer:

Question :-

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

Find Out :-

• (1) What is the value of ∠x ?
• (2) What is the value of ∠y ?
• (3) What is the value of ∠z ?
• (4) What should be the value of ∠x + 2z ?
• (5) What is the relation between y & z ?

Solution :-

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

Step by step :-

➙ ∠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°  

➙ 5y = 120°

➙ $\sf y = \dfrac{120}{5}$

➙ y = 24° -----(ii)

Again, putting value of 'y' in equation (i)

➙ $\sf 4 \times y = x$

➙ $\sf 4 \times 24 = x$

➙ $\sf 96 = x$

➙ x = 96°

Again,

➙ ∠AOD = ∠BOC (vertically opposite angles)

➙ 2z = 60° + y

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

➙ 2z = 60° + 24°

➙ 2z = 84°

➙ $\sf z =\dfrac{84}{2}$

➙ z = 42°

Solution Completed :)

Now come to question part :-

❶ Value of ∠x = 96° (b)

❷ Value of ∠y = 24° (d)

❸ Value of ∠z = 42° (c)

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

❺ Relation between y & z = 2y + z = 90° (a)

Solution for 5 :-

➙ x + 2z = 96 + 2(42) = 180°

➙ 2(24) + 42 = 90

➙ 2y + z = 90°

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