If a transversal intersects two parallel lines, then sum of interior angles on the same side of a transversal is______

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Solution

Define interior angles and apply the same side interior angle theorem
Definition : When a transversal intersects a pair of straight lines , different angles are created. The angles that
are on the same side of the transversal
have no common vertices
lie between the parallel lines
are called same side interior angles or co-interior angles.
According to the same side interior angle theorem, the interior angles are always supplementary.
A pair of supplementary angles always add up to $180^{\circ}$ by their definition
Hence the sum of the interior angles on the same side of the transversal is $180^{\circ}$

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Fill in the blanks in each of the following to make the statement true:
(i) If two parallel lines are intersected by a transversal then each pair of corresponding angles are ___
(ii) If two parallel lines are intersected by a transversal, then interior angles on the same side of the transversal are ___
(iii) Two lines perpendicular to the same line are ___ to each other.
(iv) Two lines parallel to the same line are to ___ each other.

(v) If a transversal intersects a pair of lines in such a way that a pair of alternate angles are equal, then the lines are ___
(vi) If a transversal intersects a pair of lines in such a way that the sum of interior angles on the same side of transversal is $180^{0}$ , then the lines are ___

Question 96

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Q. If a transversal intersects parallel lines, then the sum of interior angles which lie on the same side of the transversal is

If two parallel lines are intersected by a transversal, then interior angles on the same side of the transversal are

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