Find the values of the unknown angles x and y in the following figures

1.	Find the values of the unknown angles x and y in the following figures :
Answer» (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°

Find the values of the unknown angles x and y in the following figures :

Answer»

(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°