In parallelogram abcd. abd=83, bda=34 and bcd=?

Use the fact that any 4-sided figure has angles that add up to 360 degrees.  Also use the fact that parallelograms cut by a transversal have alternate interior angles that are formed.  If BD is the transversal cutting the parallelogram into 2 triangles, then 180-83-34 = 63.  So angle A is 63.  In a regular quadrilateral, the opposite angles are congruent.  Therefore, angle C is also 63 (angle BCD).  The alternate interior angle theorem helps us check ourselves for accuracy.  117+117+63+63 better equal 360.  And it does!

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