In Fig. 6.31(i) and (ii), find the values of a, b and c.

Formula Used/Theory:-

→ Angle sum property

Sum of all angles of triangle is 180°

→ Exterior angle is equal to sum of interior opposite angles

In Figure (i)

⇒ b = 60° + 70° = 130° (Exterior angle property)

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

c = 180° - 130° = 50°

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

a + 130° + 30° = 180°

a = 180° - 160° = 20°

In Figure (ii)

⇒ b = 60° + 55° = 115° (Exterior angle property)

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

a = 180° - 115° = 65°

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

c + 115° + 40° = 180°

c = 180° - 155° = 25°

Result:- In figure (i) a = 20°; b = 130°;c = 50°

In figure (ii) a = 65°; b = 115°;c = 25°