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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