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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°
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Solution
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°
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