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Which statement justifies why ∠EBC measures 90°?

Given: angles ABD and DBC are complementary

Point B is on line AE between points A and E, point B is on line FD between points F and D, ray BC intersects with line AE at point B, line FD intersects with line AE at point B, the measure of angle ABD is 50 degrees, and it is given that angles ABD and DBC are complementary.

A linear pair is two adjacent, supplementary angles.
The sum of the measures of complementary angles is 90 degrees.
If two angles are vertical angles, then they are congruent.
Alternate interior angles are congruent.

Question

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tatiklisek tatiklisek · Answer 1 · 2020-06-09T18:13:17+02:00

Answer:

Option A

Step-by-step explanation:

angles ABD and DBC are complementary given

angle ABD=50 degrees given

angles ABD and DBC = 90 degrees def. of complementary

angle DBC = 40 degrees algebra (90-50=40)

angles EBF and ABD are vertical angles vertical angles postulate

angle EBF is congruent to angle ABD def. of vertical angles

angle EBF = 50 degrees def. of congruence

angles EBF and ABF are a linear pair def. of linear pair

angles EBF and ABF are supplementary def. of linear pair

angles EBF and ABF = 180 def. of supplementary

angle ABF = 130 degrees algebra (180-50=130)

angles ABF and EBD are vertical angles vertical angles postulate

angles ABF and EBD are congruent def. of vertical angles

angle EBD = 130 degrees def. of congruence

angles CBE + DBC = EBD diagram

angles CBE + DBC = 130 degrees transitive property of congruence

angle ABD = 90 algebra (130-40=90)

B is needed in the process, but the main statement that actually does the justification is A, so option A