Find the value of x in each of the following figures?

Explanation:

(i) Using Exterior angle theorem,

∠R = ∠P + ∠Q

120° = x + 2x

⇒ 3x = 120°

⇒ x = 40°

(ii) Using Triangle sum theorem Property,

∠A + ∠B + ∠C = 180°

x + 55° + 90° = 180°

x + 145° = 180°

x = 180° - 145°

⇒ x = 35°

(iii)  Using Triangle sum theorem Property,

∠P + ∠Q + ∠R = 180°

25° + 30° + x =180°

55° + x = 180°

x = 180° - 55°

⇒ x = 125°

Final Answer:

Hence, The values of x in the given figures are 40°, 35°, 125° respectively.