Q.

In the following figure, AB || CD. If ∠ABR = 45° and ∠ROD = 105°, then find ∠ODC:
Lines and Angles Class 9 Extra Questions Maths Chapter 6 with Solutions Answers 11

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a

80°

b

100°

c

110°

d

30°

answer is B.

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Detailed Solution


Lines and Angles Class 9 Extra Questions Maths Chapter 6 with Solutions Answers 12

Through O, draw a line ‘l’ parallel to AB.
⇒ line I will also parallel to CD, then
∠1 = 45°..   [alternate int. angles]
∠1 + ∠2 + 105° = 180°  ..  [straight angle]
∠2 = 180° – 105° – 45°
⇒ ∠2 = 30°
Now, ∠ODC = ∠2 ..  [alternate int. angles]
= ∠ODC = 30°

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In the following figure, AB || CD. If ∠ABR = 45° and ∠ROD = 105°, then find ∠ODC: