6. In the adjoining figure, it is given that CE || BA, ∆BAC = 80° and ∆ECD = 35°. Find (i) ∆ACE, (ii) ∆ACB, (iii) ∆ABC.
Answers
Answered by
3
From the question,
CE∥BA,∠BAC=80
o
,∠ECD=35
o
Now,
(i) ∠BAC=∠ACE=80
o
....[∴ Alternate angles]
(ii) ∠ACB,
=∠ACB+∠ACD=180
o
....[∴ Linear pair]
=∠ACB+∠ACE+∠ECD=180
o
=∠ACB+80+35=180
=∠ACB+125=180
=∠ACB=180−115
=∠ACB=65
o
(iii) ∠ABC
Let us consider △ABC,
∠ABC+∠ACB+∠BAC=180
o
=∠ABC+65+80=180
o
=∠ABC+145=180
=∠ABC=180−145
=∠ABC=35
o
Answered by
1
Step-by-step explanation:
Solution
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From the question,
CE∥BA,∠BAC=80
o
,∠ECD=35
o
Now,
(i) ∠BAC=∠ACE=80
o
....[∴ Alternate angles]
(ii) ∠ACB,
=∠ACB+∠ACD=180
o
....[∴ Linear pair]
=∠ACB+∠ACE+∠ECD=180
o
=∠ACB+80+35=180
=∠ACB+125=180
=∠ACB=180−115
=∠ACB=65
o
(iii) ∠ABC
Let us consider △ABC,
∠ABC+∠ACB+∠BAC=180
o
=∠ABC+65+80=180
o
=∠ABC+145=180
=∠ABC=180−145
=∠ABC=35
o
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