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Example 9: In the following figure AB || CD. Calculate x, y, z.

A B
x z
y

30° 70°
C D
Solution: We have, x = 30° (Alternate interior angles)
x + y = 70° (Alternate interior angles)
⇒ 30° + y = 70°

y = 70° − 30° = 40°
Now, x + y + z = 180° (Linear pair of angles)

(x + y) + z = 180°
70° + z = 180° [(x + y) = 70° pair of alternate angles]

z = 180° − 70°
z = 110°

Thus, x = 30°, y = 40° and z = 110°
Example 10: In the given figure, the arms of two angles are parallel.
If ∠ABC = 70º, then find (a) ∠DGC (b) ∠DEF

A

D

70°
B G C

E F
Solution: (a) Consider that AB|| DG and a transversal line BC intersects them.
∠DGC = ∠ABC (Corresponding angles)

\ ∠DGC = 70°
(b) Consider that BC|| EF and a transversal line DE intersects them.

∠DEF = ∠DGC (Corresponding angles)
\ ∠DEF = 70°

Example 11: The legs of a stool makes an angle of 35° with the floor, as shown in the figure. Find
the angles x and y.

x y

35°

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