Page 57 - Ganit Kaushal

Ex 24. Name the following angles associated with the given figure using three letters.

(a) ∠1 (b) ∠2 (c) ∠3
(d) ∠1 + ∠2 (e) ∠2 + ∠3 (f) ∠1 + ∠2 + ∠3
(g) ∠CBA – ∠1
Sol. We observe in the figure,
(a) ∠1 = ∠CBD (b) ∠2 = ∠DBE (c) ∠3 = ∠EBA

(d) ∠1 + ∠2 = ∠CBD + ∠DBE = ∠CBE (e) ∠2 + ∠3 = ∠DBE + ∠EBA = ∠DBA
(f) ∠1 + ∠2 + ∠3 = ∠CBD + ∠DBE + ∠EBA = ∠CBA (or ∠ABC)
(g) ∠CBA – ∠1 = ∠CBA – ∠CBD = ∠DBA (or ∠ABD)
Ex 25. In the given figure,
(a) What is AE + EC? (b) What is AC – EC?
(c) What is BD – BE? (d) What is BD – DE?
Sol. In the given figure:

(a) AE + EC = AC (b) AC – EC = AE (c) BD – BE = ED (d) BD – DE = BE
Ex 26. Where will the hand (hour or minute, any) of a clock stop if it:
1
(a) Starts at 12 and makes of the revolution clockwise?
2
1
(b) Starts at 2 and makes of a revolution clockwise?
2
1
(c) Starts at 5 and makes of a revolution clockwise?
4
3
(d) Starts at 5 and makes of a revolution clockwise?
4
1
Sol. (a) Starting from 12 and making of a revolution clockwise, the hand of the clock
2
will stop at 6, as shown in the adjoining figure.

1
(b) Starting from 2 and making of a revolution clockwise, the hand of a clock
2
will stop at 8, as shown in the adjoining figure.

(c) Starting from 5 and making 1 of a revolution clockwise, the hand of a clock
4
will stop at 8, as shown in the adjoining figure.

(d) Starting from 5 and making 3 of a revolution clockwise, the hand of the clock
4
will stop at 2, as shown in the adjoining figure.

Lines and Angles 55