Page 157 - Start Up Mathematics_7

6. If two parallel lines l and m are cut by a transversal t, then: t

(a) each pair of corresponding angles are equal, i.e., 1 2
∠1 = ∠5, ∠2 = ∠6, ∠3 = ∠7 and ∠4 = ∠8. l
4 3
(b) each pair of alternate (interior or exterior) angles are equal, 5
i.e., ∠3 = ∠5, ∠4 = ∠6, ∠1 = ∠7, ∠2 = ∠8. 6 m
8 7
(c) each pair of interior angles on the same side of the transversal
is supplementary, i.e., ∠3 + ∠6 = 180°, ∠4 + ∠5 = 180°.
7. Conversely, when a transversal cuts two lines such that either

(a) any pair of corresponding angles are equal,
(b) any pair of alternate (interior or exterior) angles are equal, or

(c) sum of any pair of interior angles on the same side of the transversal is supplementary,
then the lines have to be parallel.

Review Exercises

Multiple ChoiCe Questions
1. The complement of an angle measuring 10° is:
(a) 0° (b) 45° (c) 80° (d) 170°

2. An angle measuring 10° more than its supplement is:
(a) 190° (b) 100° (c) 95° (d) 85°
3. Two supplementary angles are such that one is three times the other. The greater of the two
angles is:
(a) 45° (b) 90° (c) 120° (d) 135°

4. The difference between supplement of 150° and complement of 60° is:
(a) 0° (b) 30° (c) 90° (d) 210°
5. The supplement of the complement of an angle measuring 15° is:
(a) 75° (b) 105° (c) 15° (d) 90°

6. The angle which forms an alternate interior pair with angle ‘x’ as a
shown in the given figure is: b
(a) b (b) a x y

(c) y (d) z z

7. If a transversal is perpendicular to one of the two parallel lines, then the angle made by the
transversal with the other line is:
(a) 45° (b) 60° (c) 90° (d) can take any value
8. In the given figure, if p || q then the value of x is:
p
(a) 85° (b) 90° 110° 2x – 60°
q
(c) 100° (d) 135°

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