Question

prove that sum of two consecutive angle are 180

Answer 1

In parallelogram, the sum of adjacent angles is always supplementary.



In the above figure, ABCD is a parallelogram.


To prove => $\angle{A}$ + $\angle{B}$ = $\angle{B}$ + $\angle{C}$ = $\angle{C}$ + $\angle{D}$ = $\angle{D}$ + $\angle{A}$ = 180°



We know that, opposite sides of parallelogram are parallel. [Property of parallelogram]


$\therefore{}$ AB // CD


$\angle{DAB}$ + $\angle{ABC}$ = 180° (Sum of consecutive interior angles is supplementary)


$\therefore{}$ $\angle{A}$ + $\angle{B}$ = 180°


Similarly, $\angle{B}$ + $\angle{C}$ = 180° , $\angle{C}$ + $\angle{D}$ = 180° , $\angle{A}$ + $\angle{D}$ = 180°


Hence, the adjacent sides of parallelogram are supplementary.



Hence, proved.

Answer 2

Answer:

Step-by-step explanation:

The convective angles are called supplimentry angles

Eg. Angle ABC+ Angle EFG =180degree it is a supplimentry angle

Hope you can understand the concept

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