Q.1 Find the value of the unknown x in the following diagrams:

(i) we know that sum of all angle of a triangle = 180
\(\angle \) x + 50° + 60° = 180°
Or, \(\angle \) x + 110° = 180°
\(\therefore \) \(\angle \)x = 180° – 110° = 70°

(ii) we know that sum of all angle of a triangle = 180
\(\angle \)x + 90° + 30 = 180° [\(\triangle \) is right angled triangle]
Or, \(\angle \)x + 120° = 180°
Or, \(\angle \)x – 180° – 120° = 60°
(iii) we know that sum of all angle of a triangle = 180
\(\angle \)x + 30° + 110° =180°
Or, \(\angle \)x + 140° = 180°
\(\therefore \) \(\angle \)x = 180° – 140° = 40°

(iv ) we know that sum of all angle of a triangle = 180
\(\angle \)x + \(\angle \)x + 50° = 180°
Or, 2x + 50° = 180°
Or, 2x = 180° – 50°
Or, 2x = 130°
\(\therefore \) x=130/2=65°

(v) we know that sum of all angle of a triangle = 180
\(\angle \)x + \(\angle \)x +\(\angle \)x =180°
Or, 3 \(\angle \)x = 180°
\(\therefore \) \(\angle \)x=180°/3=60°

(vi) we know that sum of all angle of a triangle = 180
x + 2 x + 90° = 180° (\(\triangle \) is right angled triangle)
Or, 3x + 90° = 180°
Or, 3x = 180° – 90°
Or, 3x = 90°
\(\therefore \) x=90/3=30°