Q4 of 115 Page 8

In Fig 8.108, show that AB|| EF.

Produce EF to intersect AC at K

Now,

∠DCE + ∠CEF = 35^o + 145^o

= 180^o

Therefore, EF ‖ CD (Since, sum of co-interior angles is 180^o) (i)

Now,

∠BAC = ∠ACD = 57^o

BA ‖ CD (Therefore, alternate angles are equal) (ii)

From (i) and (ii), we get

AB ‖ EF (Lines parallel to the same line are parallel to each other)

Hence, proved

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.

In Fig 8.109, if AB ||CD and CD||EF, find ∠ACE.

In Fig 8.110, PQ||AB and PR||BC. If ∠QPR = 102°, determine ∠ABC. Give reasons.