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