Question

in the given figure l parallel to m find the value of a b c​

Answer 1

Answer:

Step-by-step explanation:

In figure (i)

∠a=180°-(120°+40°)

=180°-160°=20°

∠c=120°(alternate interior angles are equal)

∠b=40°(alternate interior angles are equal)

Therefore, ∠a=20°,∠b=40°,∠c=120°

In figure (ii)

∠b=180°-(45°+55°)

=180°-100°=80°

∠a=45°(alternate interior angles are equal)

∠c=55°(alternate interior angles are equal)

Therefore, ∠a=45°,b=80°,∠c=55°

Hope this might help you....

Answer 2

Step-by-step explanation:  

Given: The corresponding figures (i) and (ii)  

Line l parallel to m.  

To Find: Values of $\angle a,\angle b\ and\ \angle c.$  

Figure (i)  

• We know, The angles that lie on the inner side of the parallel lines but on the opposite sides of the transversal are known as the alternate interior angles. Hence, $\angle b=40^\circ$

• By angle sum property of triangles, all angles in a triangle have a sum equal to 180°. Therefore,

      ⇒ $\angle 120^\circ +\angle40^\circ+\angle a=180^\circ$  

      ⇒ $\angle 160^\circ+\angle a=180^\circ$  

     ⇒ $\angle a=180^\circ-\angle 160^\circ$  

     ⇒ $\angle a=20$°  

• We know that the sum of all angles formed in a line is 180° (linear pair). Therefore,

    ⇒ $\angle a+\angle b+\angle c=180^\circ$  

   ⇒ $\angle 20^\circ+\angle 40^\circ + \angle c=180^\circ$  

   ⇒ $\angle 60^\circ + \angle c=180^\circ$  

   ⇒ $\angle c=180^\circ-\angle 60^\circ$  

   ⇒ $\angle c=120$°  

Hence, in figure (i) $\angle a=20^\circ,\angle b=40^\circ and\ \angle c=120^\circ.$  

Figure (ii)  

• We know, The angles that lie on the inner side of the parallel lines but on the opposite sides of the transversal are known as the alternate interior angles. Hence, $\angle c=55^\circ and\ \angle a=45$°

• We know that the sum of all angles formed in a line is 180° (linear pair). Therefore,

   ⇒ $\angle a+\angle b+\angle c=180^\circ$  

   ⇒ $\angle 45^\circ+\angle b+\angle 55^\circ=180^\circ$  

   ⇒ $100 ^\circ+\angle b=180^\circ$  

   ⇒ $\angle b= 180^\circ-\angle100^\circ$  

   ⇒ $\angle b=80$°  

Hence, in figure (ii) $\angle a=45^\circ,\angle b=80^\circ and\ \angle c=55^\circ$