Question

Side BC of ∆ABC has been produced to D on left and to E on right hand side

of BC such that

∠ABD = 125° and ∠ACE = 130°. Then ∠A = ?

(a) 50° (b) 55° (c) 65° (d) 75°​

Answer 1

Answer:

b) 55°

Step-by-step explanation:

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Answer 2

Answer:

75

Step-by-step explanation:

∴  

∠

A

B

D

+

∠

A

B

C

=

180

°

∵

D

E

i

s

a

s

t

r

a

i

g

h

t

l

i

n

e

⇒

125

°

+

∠

A

B

C

=

180

°

⇒

∠

A

B

C

=

55

∘

Also,

∠

A

C

E

+

∠

A

C

B

=

180

°

⇒

130

°

+

∠

A

C

B

=

180

°

⇒

∠

A

C

B

=

50

°

∴

∠

B

A

C

+

∠

A

B

C

+

∠

A

C

B

=

180

∘

Sum of the angles of a triangle

⇒  

∠

B

A

C

+

55

°

+

50

°

=

180

°

⇒

∠

B

A

C

=

75

°

⇒

∠

A

=

75

∘