Question

parallelogram ABCD
ABCD , prove that
The sum

of any
two consecutive angles is 180 degree​

Answer 1

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parallelogram ABCD

ABCD , prove that

The sum

of any

two consecutive angles is 180 degree

$\huge\mathbb\blue{SoLuTiOn}$

Since ABCD is a parallelogram,

AD || BC

Now, AD | BC and transversal AB intersects them at A and B

respectively.

∆A + ∆B = 180⁰

Sum of the interior angles on the same side of the transversal is 180°

Since ABCD is a parallelogram, AB || DC

Now, AB || DC and transversal AC intersects them at A and C respectively.

∆C + ∆D = 180⁰

Sum of the interior angles on the same side of the transversal is 180°

Now, AD || BC and transversal AC intersects them at A and C respectively

∆A + ∆D = 180⁰

Sum of the interior angles on the same side of the transversal is 180°

Now,DC || AB and transversal BD intersects them at B and D respectively.

∆B + ∆D = 180⁰

Sum of the interior angles on the same side of the transversal is 180°

Hence proved✓