prove that the sum of all angles around a point is 360 degree
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The proof is explained step-wise below :
Step-by-step explanation:
Let AB & CD be lines intersecting at O.
Now, Sum of two angles forming a linear pair is supplementary.
⇒ m∠AOC + ∠AOD = 180° .........(1)
Also, m∠BOC + m∠BOD = 180° ..........(2)
Adding the equations,
m∠AOC + ∠AOD + m∠BOC + m∠BOD = 180° + 180°
= 360°
Therefore, all angles around O sum up to 360°
Hence Proved.
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