Q.12 Find the values of the angles x, y and z in each of the following:

(i) (ii)

(i) (ii)

From Fig. 1. we have

\(\angle \)x = 55° (Vertically opposite angles)

\(\angle \) x + \(\angle \) y = 180° (Adjacent angles)

55° + \(\angle \) y = 180° (Linear pair angles)

So, \(\angle \) y = 180° – 55° = 125°

\(\angle \) y = \(\angle \) z (Vertically opposite angles)

\(\angle \) z = 125 °

Hence, \(\angle \) x = 55°, \(\angle \) y = 125° and \(\angle \) z = 125°

From Fig. ii . we have

25° + x + 40° = 180° (Sum of adjacent angles on straight line)

65° + x = 180°

So, x = 180° – 65° = 115°

40° + y = 180° (Linear pairs)

So, y = 180° – 40° = 140°

y + z = 180° (Linear pairs)

140° + z = 180°

So, z = 180° – 140° = 40°

Hence, x – 115°, y = 140° and z – 40°