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

(a) 94°

(b) 54°

(c) 40°

(d) 44°

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Solution

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

Here, we need to find

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

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

Further, using angle sum property in ΔABC

Thus,

Therefore, the correct option is (c).

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The base BC of triangle ABC is produced both ways and the measure of exterior angles formed are 94° and 126°. Then, ∠BAC = (a) 94° (b) 54° (c) 40° (d) 44°

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

(a) 94°

(b) 54°

(c) 40°

(d) 44°