Question

the measure of Angle B E C is (2 x + 3) degrees and x = 30, which expression could represent the measure of Angle A E D?

Lines A C and B D intersect at point E.
(4 x minus 3) degrees
(3 x minus 27) degrees
(5 x minus 33) degrees
(x + 43) degrees

Answer 1

Lines AC and BD intersect, so ∠BEC and ∠AED are vertical angles and therefore equal. ∠BEC = 2x + 3 = 2(30) + 3 = 63°.

Evaluate the choices at x = 30:
- 4x − 3 = 117
- 3x − 27 = 90 − 27 = 63
- 5x − 33 = 117
- x + 43 = 73

So (3x − 27) degrees is the correct expression.