(i) In a triangle, exterior angle and adjacent internal angle make a linear pair.
x + 110° = 180°
⇒ x = 180° – 110° = 70°
In a triangle, sum of all angles is 180°.
∴ x + y + 60° = 180°
⇒ 70° + y + 60° = 180°
⇒ y + 130° = 180°
⇒ y = 180° – 130° = 50°
∴ x = 70°, y = 50°
(ii) In a triangle, exterior angle and adjacent internal angle make a linear pair.
x = 45° + 30° = 75°
∵ In a triangle, sum of all angles is 180°.
∴ y + 45° + 30° = 180°
⇒ y + 75° = 180°
∴ y = 180° – 75° = 105°
∴ x = 75°,y= 105°
(iii) In a triangle, exterior angle and adjacent internal angle make a linear pair.
∴ y + 80° = 180°
⇒ y = 180° – 80° = 100°
In a triangle, sum of all angles is 180°
∴ x + x + y = 180°
⇒ 2x + 100° = 180°
⇒ 2x = 180° – 100°
⇒ 2x = 80°
∴ x = 80°/2 = 40°
∴ x = 40°, y = 100°
(iv) Here x = 70° (vertically opposite angle)
∵ Sum of three angles of a triangle = 180°
∴ x + y + 40° = 180°
⇒ 70° + y + 40° = 180°
⇒ 110° + y = 180°
∴ y = 180° – 110° = 70°
∴ x = 70°,y = 70°