10. Chapter 10. Lines and Angles NIOS Class 10 Mathematics Textbook Solutions

Chapter 10. Lines and Angles NIOS Class 10 Mathematics Textbook Solutions for Exam Preparation

Chapter 10. LINES AND ANGLES

CHECK YOUR PROGRESS 10.1.

1. Choose the correct answer out of the given alternatives in the following multiple choice questions :

Photo

Fig. 10.29

In Fig. 10.29, AB || CD and PQ intersects them at R and S respectively.

(i) ∠ARS and ∠BRS form

(A) a pair of alternate angles

(B) a linear pair

(C) a pair of corresponding angles

(D) a pair of vertically opposite angles

Solution: (B) a linear pair .

[ Since, AB || CD and PQ intersects them at R and S respectively.

∠ARS  and ∠BRS (A linear pair of angles) ]

(ii) ∠ARS and ∠RSD form a pair of

(A) Alternate angles   (B) Vertically opposite angles   (C) Corresponding angles   (D) Interior angles

Solution:  (A) Alternate angles .

[ Since, AB||CD and PQ intersects them at R and S respectively.

  ∠ARS =∠RSD (Alternate angles)  ]

(iii) If ∠PRB = 60° , then ∠QSC is

(A) 120°      (B) 60°     (C) 30°     (D) 90°

Solution: (B) 60°

[ Since, AB || CD and PQ intersects them at R and S respectively .

 ∠PRB=∠QSC=60° ]

(iv) In Fig. 10.30 above, AB and CD intersect at O. ∠COB is equal to

    (A) 36°      (B) 72°    (C) 108°    (D) 144°

Photo fig.10.30

Solution: (C) 108° 

[ Since,  ∠COB+∠BOD=180°

⇒∠COB+72°=180°

⇒∠COB=180°-72°=108°  ]

2. In Fig. 10.31 above, AB is a straight line. Find x

Photo 10.31

Solution: Given, ∠AOC=5x+10° and ∠BOC=5x 

Since, AB is a straight line .

 ∠AOC+∠BOC=180°

⇒5x+10°+5x=180°

⇒5x+10°+5x°=180°

⇒10x=180°-10°=170°

⇒x=170°10=17°

⇒x=17°

3. In Fig. 10.32 below, l is parallel to m. Find angles 1 to 7.

Photo Fig. 10.32

Solution: Since, l is parallel to m .

∠1+70°=180° (linear pair of angles)

⇒∠1=180°-70°

⇒∠1=110° 

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