Compute all angles of each of the figures below:

Let us name the vertices of quadrilateral

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

⇒ ∠ ADC + 80° = 180°

⇒ ∠ ADC = 180° - 80°

⇒ ∠ ADC = 100°

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

⇒ ∠ DCB + 95° = 180°

⇒ ∠ DCB = 180° - 95°

⇒ ∠ DCB = 85°

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°

⇒ ∠ A + 85° + 85° + 100° = 360°

⇒ 270° + ∠ A = 360°

⇒ ∠ A = 360° - 270°

⇒ ∠ A = 90°

∠ BAG + ∠ BAD = 180°

⇒ ∠ BAG + 90° = 180°

⇒ ∠ BAG = 180° - 90°

⇒ ∠ BAG = 90°

∠ BAG = ∠ DAF (opposite angle at a vertex)

∠ DAF = 90°

∠ DAB = ∠ GAF (opposite angle at a vertex)

∠ GAF = 90°