Answer :
Final answer:
In a parallelogram, adjacent angles are supplementary and non-adjacent angles are equal. Given that one is 83 degrees and the other is 34 degrees, we find the third angle, BDC, by solving the straight-line equation 83+34+ BDC =180. However, the resultant BDC =63 degrees matches none of the options provided (83, 97, 116, or 146 degrees).
Explanation:
In a parallelogram, adjacent angles are supplementary. Knowing that ∠ABD is 83 degrees and ∠ADB is 34 degrees, we use the fact that ∠BDA + ∠ADB + ∠BDC = 180 degrees (since they form a straight line). As ∠BDA and ∠ADB are non-adjacent angles, they are equal in a parallelogram. So, ∠BDA = 83 degrees and ∠ADB = 34 degrees, given in the problem. By plugging the values into the equation, we get 83 + 34 + ∠BDC = 180. Solving for ∠BDC gives us that ∠BDC = 63 degrees, thus, none of the options provided (83 degrees, 97 degrees, 116 degrees, or 146 degrees) are correct.
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