In Fig 8.110, PQ||AB and PR||BC. If ∠QPR = 102°, determine ∠ABC. Give reasons.
Answers
<ABC = 78°
Solution:
•Produce AB such that it intersects PR
at S.
•Given, <QPR = 102°
•Since AB || PQ
•<QPR +<BAP = 180° (Sum of co-
interior angles
between || line is 180°)
• 102° +<BAP =180°
• <BAP=180°-72°=78°
•also, PR || BC =>AP || BC
• <BAP=<ABC ( Alternate interior
angles)
• <ABC=78°
∠ABC = ∠CBK = 78°
Step-by-step explanation:
Given : PQ || AB and PR || BC , ∠QPR = 102°
Construction : 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)
∠CBK = 180° – 102°
∠CBK = 78°
∠ABC = ∠CBK = 78°
Extra information :
Parallel lines:
If two lines lie in the same plane and do not intersect when produced on either side then such lines are said to be parallel to each other.
If a transversal intersects two lines such that a pair of corresponding angles is equal then the two lines are parallel.
Hope this answer will help you…
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