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# 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°