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


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

11 votes
11 votes

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.

In the adjoining figure, m||n||p and l is a transverse , find the value of x and y-example-1
User ChromeHearts
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