Compute all angles of each of the figures below:

Let us name the vertices of quadrilateral.

∠ CDA + ∠ CDE = 180° (linear pair of angles at a vertex)

⇒ ∠ CDA + 115° = 180°

⇒ ∠ CDA = 180° - 115°

⇒ ∠ CDA = 65°

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 + 100° + 75° + 65° = 360°

⇒ 240° + ∠ A = 360°

⇒ ∠ A = 360° - 240°

⇒ ∠ A = 120°

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

⇒ ∠ DAH + 120° = 180°

⇒ ∠ DAH = 180° - 120°

⇒ ∠ DAH = 60°

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

⇒ ∠ ABG + 100° = 180°

⇒ ∠ ABG = 180° - 100°

⇒ ∠ ABG = 80°

∠ BCF + ∠ BCD = 180° (linear pair of angles at a vertex)

⇒ ∠ BCF + 75° = 180°

⇒ ∠ BCF = 180° - 75°

⇒ ∠ BCF = 105°