Question

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

Options

• 94°

•  54°

•  40°

• 44°

Answer 1

 the given problem, the exterior angles obtained on producing the base of a triangle both ways are 94°and  126°. So, let us draw ΔABC and extend the base BC, such that:

∠ACD  = 126°

∠ABE  = 94°

Here, we need to find  ∠BAC  

Now, since BCD is a straight line, using the property, “angles forming a linear pair are supplementary”, we get

∠ AC+ ∠ ACD  = 180°

  ∠ ACB + 126° = 180°

             ∠ ACB = 180° - 126°

             ∠ ACB = 54°

Similarly, EBS is a straight line, so we get,

∠ ABC + ∠ ABE = 180°

      ∠ ABC + 94° = 180°

              ∠ ABC = 180° - 94° 

                ∠ ABC = 86°

Further, using angle sum property in ΔABC

∠ ABC + ∠ ACB + ∠ BAC = 180°

         54° + 86° + ∠ BAC = 180°

                            ∠ BAC = 180° - 140°

                            ∠ BAC = 40°

Thus,   ∠ BAC = 40°