Question

In the adjoining figure, m||n||p and l is a transverse , find the value of x and y.
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Answer 1

Given that

m || n || p, l is a transversal,

Consider a,b,c angles in the figure

a = 60°

Since they are vertically opposite angles

a and x are interior angles on the same side to the transversal

So they are supplementary

⇛a+x = 180°

⇛60°+x = 180°

⇛x = 180°-60°

⇛x = 120°

x and b are linear pair

x+b = 180°

⇛b = 180°-x

⇛b = 180°-120°

⇛b = 60°

b and c are corresponding angles

b and c are equal

⇛b = c = 60°

and

c and y are vertically opposite angles

⇛y = 60°

Answer: The measure of the angle x = 120°& y = 60°.

Additional comment:

If two parallel lines Intersected by a transversal then,

Vertically opposite angles are equal. Corresponding angles are equal. Alternative interior angles are equal. Interior angles on the same side to the transversal are supplementary.