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प्रश्न
If the side BC of ΔABC is produced on both sides, then write the difference between the sum of the exterior angles so formed and ∠A.
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उत्तर
In the given problem, we need to find the difference between the sum of the exterior angles and∠A.
Now, according to the exterior angle theorem
ext. ∠C = ∠A + ∠B .........(1)
Also,
ext. ∠B = ∠A + ∠C .........(2)
Further, adding (1) and (2)
ext. ∠C + ext. ∠B = ∠A + ∠B + ∠A + ∠B
=2∠A+ ∠B + ∠C .........(3)
Also, according to the angle sum property of the triangle, we get,
∠A + ∠B + ∠C = 180° .........(4)
Now, we need to find the difference between the sum of the exterior angles and ∠A
Thus,
( ext. ∠C + ext. ∠B) - ∠A = (2∠A + ∠B + ∠C ) - ∠A
= ∠A = ∠B + ∠C
= 180°(Using 4)
Therefore, (ext. ∠C ext.∠B) -∠A = 180°
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