Q. 35.0( 1 Vote )

Compute all outer angles of the quadrilateral shown below.


Answer :

Let us name the different coordinate in the above question figure:



Sum of the angles of 4-sided polygon


Sum of the angles of n-sided polygon = (n – 2) × 180°


S = (4 – 2) × 180°


S = 2 × 180°


S = 360°


In ABCD


A + B + C + D = 360°


130° + 70° + 60° + D = 360°


260° + D = 360°


D = 360° - 260°


D = 100°


Exterior Angles


FAB + DAB = 180° (linear pair of angles at a vertex)


FAB + 130° = 180°


FAB = 180° - 130°


FAB = 50°


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


CBE + 70° = 180°


CBE = 180° - 70°


CBE = 110°


DCB + DCH = 180° (linear pair of angles at a vertex)


60° + DCH = 180°


DCH = 180° - 60°


DCH = 120°


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


ADG + 100° = 180°


ADG = 180° - 100°


ADG = 80°


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