In Fig 8.109, if AB ||CD and CD||EF, find ∠ACE.
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Given : AB || CD and CD|| EF.
To find : ∠ACE.
Proof:
Since, EF ‖ CD and EC is a transversal and sum of the interior angles on the same side of a transversal is 180°.
∴ ∠FEC + ∠ECD = 180°
130° + ∠ECD = 180°
∠ECD = 180° – 130°
∠ECD = 50°
Also, BA ‖ CD
∠BAC = ∠ACD = 70°
[Alternate angles]
But, ∠ACD = ∠ACE + ∠ECD
70° = ∠ACE + 50°
∠ACE = 70° - 50°
∠ACE = 20°
Hence , ∠ACE is 20°.
HOPE THIS ANSWER WILL HELP YOU…..
Some questions of this chapter :
In Fig 8.112, if l||m, n||p and ∠1 =85°, find ∠2.
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In Fig 8.108, show that AB|| EF.
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15
Answer:
- hope it helpss..
Step-by-step answers
Since EF ∥ CD
Therefore, EFC + ECD = 180 [co-interior angles are supplementary]
⟹ ECD = 180 - 130 = 50
Also BA ∥ CD
⟹ BAC = ACD = 70 [alternative angles]
But, ACE + ECD = 70
⟹ ACE = 70 - 50 = 20
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