In figure (i) and (ii), Find the values of a, b and c.

(i) In ∆ADC, we have

∠c + 60° + 70° = 180° (Angle sum property)

⇒ ∠c + 130° = 180°

⇒ ∠c = 180° – 130° = 50°

∠c + ∠b = 180° (Linear pair)

⇒ 50° + ∠b = 180°

⇒ ∠ b = 180° – 50° = 130°

In ∆ABD, we have

∠a + ∠b + 30° = 180° (Angle sum property)

⇒ ∠a + ∠130° + 30° = 180°

⇒ ∠a + 160° = 180°

⇒ ∠a = 180° – 160° = 20°

Hence, the required values are a = 20°, b = 130° and c = 50°

(ii) In ∆PQS, we have

∠a + 60° + 55° = 180°(Angle sum property)

⇒ ∠a + 115° = 180°

⇒ ∠a = 180° – 115°

⇒ ∠a = 65°

∠a + ∠b = 180° (Linear pair)

⇒ 65° + ∠b = 180°

⇒ ∠b = 180° – 65° = 115°

In ∆PSR, we have

∠b + ∠c + 40° = 180° (Angle sum property)

⇒ 115° + ∠c + 40° = 180°

⇒ ∠c + 155° = 180°

⇒ ∠c = 180° – 155° = 25°

Hence, the required angles are a = 65°, b = 115° and c = 25°