Question

The interior angle of point B measures (3x - 7) degrees and the interior angle of point D measures (x + 15) degrees. What is the value of x?

Answer 1

I need one detail: what figure or relation ties angles B and D together (e.g. opposite angles of a parallelogram, consecutive angles, opposite angles of a cyclic quadrilateral, etc.)? Two common interpretations:

1) If B and D are opposite angles of a parallelogram (so they’re equal):
3x − 7 = x + 15
2x = 22 → x = 11

2) If B and D are opposite angles of a cyclic quadrilateral or are consecutive interior angles that are supplementary:
(3x − 7) + (x + 15) = 180
4x + 8 = 180 → 4x = 172 → x = 43

Tell me which situation applies and I’ll confirm the correct value.