Question

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Answer 1

Step-by-step explanation:

1)

(i) If a || b then <1 = <5

Used Property :- Corresponding angles are equal.

(ii) If <4 = <5 then a||b

Used Property :-

Interior angles on the same side to the transversal are Supplementary then two lines are parallel.

(iii) If <4+<5 = 180° then a||b

Used Property :-Interior angles on the same side to the transversal are Supplementary then two lines are parallel.

2)

(i) The pairs of corresponding angles are

(<1,<5) , (<2, <6) ,(<3,<8) , (<4,<7)

(ii) The pairs of alternative interior angles are

(<2,<8) and (<3,<5)

(iii) The pairs of Interior angles on the same side to the transversal are (<3,<8) and (<2,<5)

(iv) The vertically opposite angles are

(<2,<8) and (<3,<5)

3)

Given that p||q

We know that

Vertically Opposite angles are equal

=> e = f

and

125° and f are linear pair

=> 125°+f = 180°

=> f = 180°-125°

=> f = 55°

=> e = 55°

f and a are alternative interior angles which are equal

=> e = a

=> a = 55°

c and a are alternative interior angles which are equal

=> c = a

=> c = 55°

a and b are linear pair

=> a+b = 180°

=> 55° +b = 180°

=> b = 180°-55°

=> b = 125°

125° and d are corresponding angles which are equal

=> d = 125°

Therefore,

a = 55°

b = 125°

c = 55°

d = 125°

e = 55°

f = 55°