Q. 23.5( 13 Votes )

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Answer :

• Given: Line q is transversal is to line m and line l.

• To find: (1) Interior alternate angles

(2) Corresponding angles

(3) Interior angles

(1) Now for Interior Alternate angles

Pairs of angles which are on the opposite sides of transversal and their arms on the transversal show opposite directions is called a pair of alternate angles.

When these angels are in the inner side they are called Interior alternate angels.

1) For ∠b the angle which is in the inner side as well as on the opposite side of transversal and it’s arm show opposite direction is ∠h. So ∠b and ∠h form pair of Interior Alternate angel.

2) For ∠c the angel which is in the inner side as well as on the opposite side of transversal and it’s arm show opposite direction is ∠e. So ∠c and ∠e form pair of Interior Alternate angel.

(2) Corresponding angles

If we go by the definition, the definition of corresponding angels tells us, if the arms on the transversal of a pair of angles are in the same direction and the other arms are on the same side of the transversal, then it is called a pair of corresponding angles.

So, now in the above given figure we have say, line q making transversal to line m and line l.

1)For ∠a, ∠e is the angle which is in the same side and same direction of transversal so ∠a is the corresponding angle to ∠e.

2)For ∠b, ∠f is the angle which is in the same side and same direction of transversal so ∠b is the corresponding angle to ∠f.

3)For ∠d, ∠h is the angle which is in the same side and same direction of transversal so ∠d is the corresponding angle to ∠h.

4)For ∠c, ∠g is the angle which is in the same side and same direction of transversal so ∠c is the corresponding angle to ∠g.

(3) Interior angles

A pair of angles which are on the same side of the transversal and inside the given lines is called a pair of interior angles.

So, we get only two such pairs of angels.

1) ∠b has ∠e on the same side of transversal and inside the given line. So ∠b and ∠e form pair of interior angels.

2) ∠c has ∠h on the same side of transversal and inside the given line. So ∠c and ∠h form pair of interior angels.

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