Question

In a paralleleogram ABCD angle c =105. Find the remaining angle

Answer 1

ATP
angle c = 105 °
therefore, angle d = (180 -105)° [ AB || DC]
d= 75°
since angle d= 75° and angle c=105°
therefore, angle a = 75° and angle b = 105°

Answer 2

We know that opposite angles of a parallelogram are equal.
 So, ∠a = ∠c & ∠b = ∠d ..................................................(1)

We also know that ∠a + ∠b + ∠c + ∠d = 360°  [∠s of Quadrilateral.]
                                ∠a + ∠a + ∠d + ∠d = 360° 
                     we are given ∠a = ∠c = 105°
 
    So, by putting value of ∠a
         
                          105° + 105° + 2∠d = 360°
                          so, ∠d= 360°-210°/2
                                     =  150°/2
                             so, ∠d= 75° ..................................(2 )

     By Eqn. (1) & (2)
        ∠a = ∠c = 105° and, ∠b = ∠d = 75°

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