Question

2. In a parallelogram ABCD, prove that the sum of
any two consecutive angles is 180º.
1​

Answer 1

Answer:

Step-by-step explanation:

ABCD is a parallelogram, therefore AD||BC

Now, AD||BC and transversal AB intersects them

A + B = 180o               (sum of interior angles on the same side of transversal)

Similarly you can prove that

B + C = 180o, C + D = 180o and D + A = 180o

Let ABCD be a llgm with angles a,b,c and d

So we that in a llgm opp angles are equal (1)

So,

a+b+c+d=360.(As llgm isQuadrilateral)

Let a and d be opp angles and a,b and c,d be consecutive angles

2a +2b =360°. [by (1)]

a+b=360/2=180°

Hence proved

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