The base BC of triangle ABC is produced both ways and the measure of exterior angles formed are 94° and 126°. Then, ∠ BAC =

Question

The base BC of triangle ABC is produced both ways and the measure of exterior angles formed are 94&#xB0; and 126&#xB0;. Then, &#x2220; BAC =

Philoid · Accepted Answer

Given,

∠ABD = 94^o and

∠ACE = 126^o

∠ABD + ∠ABC = 180^o (Linear pair)

∠ABC = 86^o (i)

∠ACE + ∠ACB = 180^o (Linear pair)

∠ACB = 54^o (ii)

In

∠ABC + ∠ACB + ∠BAC = 180^o

86^o + 54^o + ∠BAC = 180^o

∠BAC = 40^o