Question

6. In Fig. 8.110, PQ || AB and PR || BC. If angle QPR = 102°, determine angle ABC. Give reasons.
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Answer 1

Answer:

The required value of ∠ABC is 78°

Explanation:

Given Problem:

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

Solution:

We need to find ∠ABC

AB is produced to meet PR at K

Since, PQ ‖ AB

∠QPR = ∠BKR = 102°                     (Corresponding angles)

Since, PR ‖ BC

Therefore,

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

∠CKB = 180° – 102°

= 78°.............................................(Answer)

Answer 2

Answer:

The required value of ∠ABC is 78°

Explanation:

Given Problem:

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

Solution:

We need to find ∠ABC

AB is produced to meet PR at K

Since, PQ ‖ AB

∠QPR = ∠BKR = 102°                     (Corresponding angles)

Since, PR ‖ BC

Therefore,

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

∠CKB = 180° – 102°

= 78°.............................................(Answer)