Find the value of x from the given figure and hence find the measure of each angle of the triangle.

(i) Sum of the three angles of a triangle = 180°

∴ 2x + 30° + 60° – x + 3x – 10° = 180°

⇒ (2x – x + 3x) + (30° + 60° – 10°) = 180°

⇒ 4x + 80° = 180°

⇒ 4x = 180° – 80°

⇒ 4x = 100°

∴ x = 10004 = 25°

∴ Measure of the angles are:

(i) (2x + 30)° – 2 × 25° + 30° = 80°

(ii) (60 – x)° = 60° – 25° = 35°

(iii) (3x – 10)° = 3 × 25° – 10° = 75° – 10° = 65°

Hence, x = 25° and the angles of the triangles are: 80°, 35° and 65°.