(3) Compute all outer angles of the quadrilateral shown below. 130 70° 60°
Answers
Step-by-step explanation:
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°
