Side BC of ΔABC has been produced to D on left hand side and to E on right hand side such that ∠ABD = 125° and ∠ACE = 130°. Then ∠A = ?

Question

Side BC of ΔABC has been produced to D on left hand side and to E on right hand side such that ∠ ABD = 125° and ∠ ACE = 130 ° . Then ∠ A = ?

Philoid · Accepted Answer

ABD + ABC = 180 (Linear pair of angles)

ABC = 180^o – 125^o=55^o

ACE + ACB = 180 (Linear pair of angles)

ACB = 180^o – 130^o=50^o

As we know that

ACB + ABC + BAC = 180^o

BAC = 180 – 55 – 50

=75^o