Amisha makes a star with the help of line segments a, b, c, d, e and f, in which a ǁ d, b ǁ e and c ǁ
f. Chhaya marks an angle as 120 degrees
as shown in the given figure and Amisha to find the angle x, y
and z. Help Amisha in finding the angles.
with
explanation
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Answer:
∠1=120
o
... (1) [vertically opposite angles]
Here, c is parallel to f and a is transversal.
∠1+∠x=180
o
.... (1) [Co-interior angles]
⇒120
o
+∠x=180
o
[Using equation 1]
⇒∠x=180
o
−120
o
⇒∠x=60
o
.... (2)
Now, a is parallel to d and c is transversal
∠x+∠2=180
o
.... [Co-interior angles]
⇒60
o
+∠2=180
o
[Using equation 2]
⇒∠2=180
o
−60
o
⇒∠2=120
o
⇒∠2=120
o
=∠y ... [vertically opposite angles]
Here, a is parallel to d and f is transversal
∠1+∠z=180
o
.... [Co-interior angles]
⇒120
o
+∠z=180
o
[Using equation 1]
⇒∠z=180
o
−120
o
⇒∠z=60
o
Therefore,
∠x=60
o
∠y=120
o
∠z=60
o
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