(i) Let ∠S = 3x° 

Given = \(\overline{RS}\)

Given = \(\overline{RT}\)

= 4.5 cm 

Given ∠S = ∠T 

= 3x° [∵ Angles opposite to equal sides are equal] 

By angle sum property of a triangle we have, 

∠R + ∠S + ∠T = 180° 

72° + 3x + 3x = 180° 

72° + 6x = 180° 

x = \(\frac{108°}{6}\)

x = 18°

(ii) Given ∠X = 3x; 

∠Y = 2x; 

∠Z = 4x 

By angle sum property of a triangle we have 

∠X + ∠Y + ∠Z = 180° 

3x + 2x + 4x = 180°

∴ 9x = 180°

x = \(\frac{180°}{9}\)

x = 20°

(iii) Given ∠T = (x – 4)° 

∠U = 90° 

∠V = (3x – 2)° 

By angle sum property of a triang we have 

∠T + ∠U + ∠V = 180° 

(x – 4)° + 90° + (3x – 2)° = 180° 

x – 4° + 90° + 3x – 2° = 180° 

x + 3x + 90° – 4° – 2° = 180° 

4x + 84° = 180° 

4x = 180° – 84° 

4x = 96° 

x = \(\frac{96°}{4}\)

= 24° 

x = 24°

(iv) Given ∠N = (x + 31)° 

∠O = (3x – 10)° 

∠P = (2x – 3)°

By angle sum property of a triangle we have 

∠N + ∠O + ∠P = O 

(x + 31)° + (3x – 10)° + (2x – 3)° = 180° 

x + 31°+ 3x – 10° + 2x – 3° = 180° 

x + 3x + 2x + 31° – 10° – 3° = 180° 

6x + 18° = 180° 

6x = 180° + 18° 

6x = 162° 

x = \(\frac{162°}{6}\)

= 27° 

x = 27°