Question

Which statement justifies why EBC measures 90°? Given: angles ABD and DBC are complementary

Answer 1

The justification is: A. A linear pair is two adjacent, supplementary angles.

• Given:

$m \angle ABD and m\angle DBC$ are complementary angles,

$m \angle ABD + m\angle DBC = 90^{\circ}\\m \angle ABD + m\angle DBC = m \angle ABC$

Therefore:

$m \angle ABC= 90^{\circ}$

$\angle ABC and m\angle EBC$ are two adjacent angles on a straight line.

Therefore:

$\angle ABC + m\angle EBC = 180^{\circ}$ (supplementary angles)

Substitute

$90 + m\angle EBC = 180\\m\angle EBC = 180 - 90\\m\angle EBC = 90^{\circ}$

Therefore, the justification as to why $m\angle EBC = 90^{\circ}$ is: A. A linear pair is two adjacent, supplementary angles.

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