Chapter 6: Lines and Angles

Choose the correct answers :

Q1. If two interior angles on the same side of a transversal intersecting two parallel lines are in the ratio 2 : 3 , then the greater of the two angles is :

(A) 54°    (B) 108°     (C) 120°     (D) 136°

Ans: (B) 108°    

 [Hints : let 2x and  3x are two angles .

So, 2x+3x=180°

⇒5x=180° 

⇒x=180°5 

⇒x=36° 

 2x=2×36°=72°

And  3x=3×36°=108° ]

Q2. If one angle of a triangle is equal to the sum of the other two angles, then the triangle is :

(A) an isosceles          (B) an obtuse triangle   (C) an equilateral triangle  (D) a right triangle

Ans:  (B) an obtuse triangle   .

Q3. An exterior angle of a triangle is 105° and its two interior opposite angles are equal . Each of these equal angles is :

(A) 3712°     (B) 5212°       (C) 7212°                (D) 75°

Ans:  (B) 5212°       

 [Hints: Let x be the angle .

A/Q, x+x=105°

 ⇒2x=105°⇒x=105°2

⇒x=5212°  ]

Q4. The angles of a triangle in the ratio 5 : 3 : 7 , then the triangle is :

(A) an acute angled triangle    (B) an obtuse angled triangle

(C) a right triangle   (D) an isosceles triangle

Ans: (A) an acute angled triangle .

[Hints : Every angle of the triangle is less than 90° ]

Q5. If one of the angle of a triangle is 130°, then the angle between the bisectors of the other two angles can be :

(A) 50°     (B) 65°     (C) 145°     (D) 155°

Ans:  (B) 65°

 [Hints:  Other angle =12×130°=65° ]

Q6. In fig. 6.2 , POQ is a line . The value of x is :

(A) 20°     (B) 25°     (C) 30°      (D) 35°                

Ans :  (A) 20°   . 

[ Hints: 40°+4x+3x=180°

⇒40°+7x=180° 

⇒7x=180°+40° 

⇒7x=140° 

⇒x=140°7 

⇒x=20°  ]

Q7. In fig. 6.3 , if OP∥RS , ∠OPQ=110°  and ∠QRS=130° , then ∠PQR is equal to :

(A) 40°    (B) 50°      (C) 60°      (D) 70°  

Ans:  [ Hints:  Suppose , RS∥QX  and OP∥RS  

 So, ∠XQR+130°=180°

⇒∠XQR=180°-130°=50° 

∠PQX=110°  (Alternative interior angle)

∠PQR+50°=110° 

⇒∠PQR=110°-50° 

⇒∠PQR=60°        ]