2. In Fig. 6.29, if AB || CD, CD || EF and y : z = 3 : 7, find x.
Solution: It is known that AB || CD and CD||EF As the angles on the same side of a transversal line sums up to 180°, x + y = 180° —–(i) Also, ∠O = z (Since they are corresponding angles) and, y +∠O = 180° (Since they are a linear pair) So, y+z = 180° Now, let y = 3w and hence, z = 7w (As y : z = 3 : 7) ∴ 3w+7w = 180° Or, 10 w = 180° So, w = 18° Now, y = 3×18° = 54° and, z = 7×18° = 126° Now, angle x can be calculated from equation (i) x+y = 180° Or, x+54° = 180° ∴ x = 126°
