Q. 33.7( 3 Votes )

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Answer :


ADC + CDF = 180° (linear pair of angles at a vertex)


CDF = 180° - ADC …(1)


ABC + CBE = 180° (linear pair of angles at a vertex)


CBE = 180° - ABC … (2)


Sum of two exterior angles marked.


CBE + CDF = 180° - ABC + 180° - ADC


CBE + CDF = 360° - ( ABC + ADC) …(3)


In ABCD


ABC + BCD + ADC + DAB = 360°


[sum of all interior angles 4-sided polygon is 360°]


ABC + ADC = 360° - BCD - DAB


Put this value in equation (3)


CBE + CDF = 360° - (360° - BCD - DAB)


CBE + CDF = 360° - 360° + BCD + DAB


CBE + CDF = BCD + DAB


Hence, yes there is a relation between the sum of exterior angles marked and sum of inner angles at the other two vertices.


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