Page 147 - Start Up Mathematics_7

Example 23: In the adjoining figure:
A C
(a) Is ∠3 adjacent to ∠4?
1
(b) Is ∠COE adjacent to ∠COB? 2

(c) Does ∠COE and ∠EOD form a linear pair? 5 O
3 E
(d) Are ∠BOD and ∠DOA supplementary?
(e) Is ∠1 vertically opposite to ∠4? 4
(f) Which angle is vertically opposite to ∠5? D B
(g) Are ∠1 and ∠3 vertically opposite angles?

Solution: (a) Yes, ∠3 and ∠4 are adjacent.
(b) No, ∠COE and ∠COB are not adjacent.
(c) Yes, ∠COE and ∠EOD form a linear pair. 1 2
(d) Yes, ∠BOD and ∠DOA are supplementary. 3
(e) Yes, ∠1 and ∠4 are vertically opposite angles. 5 4
(f) ∠COB is vertically opposite to ∠5.
(g) No, ∠1 and ∠3 are not vertically opposite angles.
Example 24: Indicate all pairs of angles that form:
(a) Vertically opposite angles
(b) Linear pair
Solution: (a) ∠3 and ∠5; ∠4 and (∠1 + ∠2) are vertically opposite angles.
(b) ∠4 and ∠5; ∠3 and ∠4 are linear pairs.

Example 25: Find the values of the angles x, y and z in each of the following:

y

105° x
(a) (b) x

z 30°
z
y

Solution: (a) x = 105° (Vertically opposite angles)
y + 105° = 180° (Linear pair)

∴ y = 75°
z = y = 75° (Vertically opposite angles)
(b) 30° + y = 180° (Linear pair)
⇒ y = 150°

z = 30° (Vertically opposite angles)
(30° + x) + 90° = 180° (Linear pair)

⇒ 30° + x = 90°
⇒ x = 90° – 30° = 60°

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