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

Question

In Fig 8.110, PQ||AB and PR||BC. If &#x2220; QPR = 102&#xB0;, determine &#x2220; ABC . Give reasons.

Philoid · Accepted Answer

AB is produced to meet PR at K

Since, PQ ‖ AB

∠QPR = ∠BKR = 102^o (Corresponding angles)

Since, PR ‖ BC

Therefore,

∠RKB + ∠CBK = 180^o (Co. interior angles)

∠CKB = 180^o – 102^o

= 78^o