In the given figure, AG is a straight line. Find the value of ∠1 + �

1.	In the given figure, AG is a straight line. Find the value of ∠1 + ∠2 + ∠3 + ∠4 + ∠5 + ∠6.FigureTransversalExterior anglesInterior anglesPairs of corresponding anglesPairs of alternative interior anglesPairs of alternative exterior angles(i)n∠a, ∠b∠h, ∠g∠c, ∠d∠e, ∠f ∠b, ∠f ; ∠c, ∠g∠a, ∠e ; ∠d, ∠h∠c, ∠e∠d, ∠f∠a, ∠g∠b, ∠h(ii)r∠1, ∠4,∠5, ∠8∠2, ∠3∠6, ∠7∠1, ∠3∠2, ∠4∠5, ∠7∠6, ∠8∠2, ∠6∠3, ∠7∠1, ∠5∠4, ∠8
Answer» Given ∠AOC and ∠COG are linear pair. ∠AOC + ∠COG = 180° (linear pair) But ∠AOC = ∠AOB + ∠BOC = ∠1 + ∠2 ∠COG – ∠COD + ∠DOE + ∠EOF + ∠FOG – ∠3 + ∠4 + ∠5 + ∠6 => (∠AOB + ∠BOC) + (∠COD + ∠DOE + ∠EOF + ∠FOG) = 180° => ∠1 + ∠2 + ∠3 + ∠4 + ∠5 + ∠6 = 180° Therefore, the sum of angles at a point on the same side of the line is 180°.

In the given figure, AG is a straight line. Find the value of ∠1 + ∠2 + ∠3 + ∠4 + ∠5 + ∠6.FigureTransversalExterior anglesInterior anglesPairs of corresponding anglesPairs of alternative interior anglesPairs of alternative exterior angles(i)n∠a, ∠b∠h, ∠g∠c, ∠d∠e, ∠f ∠b, ∠f ; ∠c, ∠g∠a, ∠e ; ∠d, ∠h∠c, ∠e∠d, ∠f∠a, ∠g∠b, ∠h(ii)r∠1, ∠4,∠5, ∠8∠2, ∠3∠6, ∠7∠1, ∠3∠2, ∠4∠5, ∠7∠6, ∠8∠2, ∠6∠3, ∠7∠1, ∠5∠4, ∠8

Answer»

Given ∠AOC and ∠COG are linear pair.

∠AOC + ∠COG = 180° (linear pair)

But ∠AOC = ∠AOB + ∠BOC

= ∠1 + ∠2 ∠COG – ∠COD + ∠DOE + ∠EOF + ∠FOG – ∠3 + ∠4 + ∠5 + ∠6

=> (∠AOB + ∠BOC) + (∠COD + ∠DOE + ∠EOF + ∠FOG) = 180°

=> ∠1 + ∠2 + ∠3 + ∠4 + ∠5 + ∠6 = 180°

Therefore, the sum of angles at a point on the same side of the line is 180°.