Q1 of 115 Page 8

In Fig 8.105, AB, CD and ∠1 and ∠2 are in the ratio 3 : 2. Determine all angles from 1 to 8.

Let, ∠1 = 3x

∠2 = 2x

∠1 + ∠2 = 180^o(Linear pair)

3x + 2x = 180^o

5x = 180^o

x = 36^o

Therefore,

∠1 = 3x = 108^o

∠2 = 2x = 72^o

Vertically opposite angles are equal, so:

∠1 = ∠3 = 108^o

∠2 = ∠4 = 72^o

∠5 = ∠7 = 108^o

∠6 = ∠8 = 72^o

Corresponding angles:

∠1 = ∠5 = 108^o

∠2 = ∠6 = 72^o

Which of the following statements are true (T) and which are false (F)?

(i) Angles forming a linear pair are supplementary.

(ii) If two adjacent angles are equal, then each angle measures 90°.

(iii) Angles forming a linear pair can both be acute angles.

(iv) If angles forming a linear pair are equal, then each of these angles is of measure 90°.

Fill in the blanks so as to make the following statements true:

(i) If one angle of a linear pair is acute, then its other angle will be ………..

(ii) A ray stands on a line, then the sum of the two adjacent angles so formed is …………

(iii) If the sum of two adjacent angles is 180°, then the ………….arms of the two angles are opposites rays.

In Fig 8.106, l, m and n are parallel lines intersected by transversal p at X, Y and and Z respectively. Find ∠1, ∠2 and∠3.

In Fig 8.107, AB ||CD ||EF and GH ||KL. Find ∠HKL.