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Solution: Given, the legs of a stool makes an angle of 35° with the floor.

We need to find the angles x and y. S P l
x y
Considering l and m are parallel and PQ is a transversal,
O
If two parallel lines are intersected by a transversal, each pair of alternate 35° m
interior angles are equal. Q R

So, ∠x = ∠PQR

∠x = 35°

We know that the sum of a linear pair of angles is always equal to 180°.

So, ∠x + ∠y = 180°

35° + ∠y = 180°

∠y = 180° – 35°
∠y = 145°

Therefore, the measures of ∠x and ∠y are 35° and 145°, respectively.

Checking for Parallel Lines

A draftsman uses a carpenter’s square and a straight edge (ruler) to draw line

segments as shown in the adjoining figure. He claims they are parallel. How?

Are you able to see that he has kept the corresponding angles to be equal?
(What is the transversal here?)

• When a transversal cuts two lines, such that pairs of corresponding angles are
equal, then the lines are said to be parallel.

Also, look at the letter Z. The horizontal segments here are parallel,
because the alternate angles are equal.

• When a transversal cuts two lines, such that pairs of alternate interior
angles are equal, the lines are said to be parallel. p
1
Now, let us draw a line l and also draw a line m perpendicular to l.

Again draw a line p, such that p is perpendicular to m. 2 l

Thus, p is perpendicular to a perpendicular to l. m

So, ∠1 + ∠2 = 180°.

• When a transversal cuts two lines, such that pairs of interior angles on the same side of the transversal
are supplementary, the lines are said to be parallel.

159 Lines and Angles