Question

In the given figure line AB || line CD and measure of angle1= 65o .Find the measure of all the angles marked in the figure. Justify your answer.​

Answer 1

Answer:

60°

Step-by-step explanation:

Given,

CD ║ AB

⇒ CD ║ AF ( shown in the given diagram ),

Let ∠x and ∠DCE are linear pairs,

⇒ ∠x + m∠DCE= 180°,

⇒ ∠x + 75° = 180° ( by the diagram ),

⇒ ∠x = 180° - 75° = 105°,

By the alternate interior angle theorem,

∠x ≅ ∠1,

⇒ m∠x = m∠1

⇒ m∠1 = 105°,

Now, by the vertically opposite angle theorem,

∠1 ≅ ∠BEO,

⇒ m∠BEO = 105°,

Now, m∠EBO = 15°,

∵ BEO is a triangle,

⇒ m∠EBO + m∠BEO + m∠BOE = 180°,

⇒ 15° + 105° + m∠BOE = 180°,

⇒ 120° + m∠BOE = 180°,

⇒ m∠BOE = 60°,

⇒ m∠BOC = 60°,

Answer 2

Answer:

AB∣∣CD

EF is transversal

∠AGE=45°

∠EGB+45=180

⟹∠EGB=135 °

∠AGH=135 °

∠AGH=135 °

⟹∠GHC=45

∠GHD=135

∠DHF=45

∠FHC=135

∠GHC=45

hope it helps you