i) In ΔPQR

x° + 50° = 120° (exterior angle property) 

x°= 120°- 50° 

x°= 70° 

Also ∠P + ∠Q +∠R = 180° (angle – sum property) 

70° + 50° + y° = 180° 

120° + y° = 180° 

y° = 180° – 120° 

y° = 60°

(OR)

y° + 120° = 1800 (linear pair of angles) 

y° = 180°- 120° 

∴ y° = 60°

ii) In the figure ΔRST, 

x° = 80° (vertically opposite angles) 

also ∠R + ∠S + ∠T = 180° (angle – sum property) 

80° + 50°+ y°= 180° 

130° + y° = 180° 

y° = 180° – 130° 

∴ y° = 50°

iii) m ΔMAN, 

x° = ∠M + ∠A (exterior angle property) 

x° = 50° + 60° 

x° = 110° 

Also x° + y° = 180° 

110°+ y°= 180° 

y° = 180° – 110° 

y° = 70°

(OR) 

in ΔMAN, 

∠M + ∠A + ∠N = 180° (angle – sum property )

50° + 60° + y° = 180° 

110° + y° = 180° 

y° = 180°- 110° 

∴ y° = 70°

v) In the figure ΔABC, 

x° = 60° (vertically opposite angles) 

∠A + ∠B + ∠ACB = 180° (angle – sum property) 

y° + 30° + 60° = 180° 

y° + 90° = 180° 

y° = 180° – 90° 

∴ y° = 90°

v) In the figure ΔEFG, 

y° = 90° (vertically opposite angles)

Also in ΔEFG; 

∠F + ∠E + ∠G = 180° (angle – sum property) 

∴ x° + x° + y° = 180 

2x° + 90° = 180° 

2x° = 180°- 90° 

2x° = 90°

x° = 90°/2

∴ x° = 45°

vi) In the figure ΔLET, 

∠L = ∠T = ∠E = x° (vertically opposite angles) 

Also in ΔLET 

∠L + ∠E + ∠T = 180° (angle – sum property) 

x° + x° + x° = 180° 

3x° = 180°

x° = 180°/3

x° = 60°