Question

Amish makes a star with the help of line segments a, b, c, d, e,  and f, in which a∥d, b∥e and c ∥ f . Chhaya makes an angle as 120o as shown fig., and asks Amisha to find the ∠x,∠yand ∠z.
Help AMish in finding the angles.​

Answer 1

∠1=120o ... (1) [vertically opposite angles]

Here, c is parallel to f and a is  transversal.

∠1+∠x=180o .... (1) [Co-interior angles]

⇒120o+∠x=180o [Using equation 1]

⇒∠x=180o−120o

⇒∠x=60o .... (2)

Now, a is parallel to d and c is transversal

∠x+∠2=180o ....  [Co-interior angles]

⇒60o+∠2=180o [Using equation 2]

⇒∠2=180o−60o

⇒∠2=120o 

⇒∠2=120o=∠y ... [vertically opposite angles]

Here, a is parallel to d and f is transversal

∠1+∠z=180o ....  [Co-interior angles]

⇒120o+∠z=180o [Using equation 1]

⇒∠z=180o−120o

⇒∠z=60o 

Therefore,

∠x=60o

∠y=120o  

∠z=60o

Answer 2

$★Question$

Amish makes a star with the help of line segments a, b, c, d, e,  and f, in which a∥d, b∥e and c ∥ f . Chhaya makes an angle as 120o as shown fig., and asks Amisha to find the ∠x,∠yand ∠z.

Help AMish in finding the angles.

$‡Answer = >$

∠A = 1200 (Vertically Opposite )

∠A + ∠ x = 1800 (Co-interior angle)

⇒ ∠x = 600

∠B + ∠ x = 1800 (Co-interior angle)

∠B = 1200

⇒ ∠y = 1200 (Vertically Opposite angle)

∠ z = ∠x = 600 (Alternate interior angle)

∠x = 600, ∠y = 1200, ∠z = 600

Hence,

• ∠x = 600,
• ∠y = 1200,
• ∠z = 600

@shwetasingh1421977.