Question

complete this sentence with the best of the choices given.

if the exterior sides of adjacent angles are perpendicular, the angles are ______.

after you pick your answer press go.

a. supplementary b. congruent
c. right angles d. complementary
e. obtuse

Explanation:

1. Recall the definition of adjacent angles with perpendicular exterior sides: If the exterior sides of adjacent angles are perpendicular, the angle between them is \(90^\circ\).
2. Analyze the sum of adjacent angles: Let the two adjacent angles be \(\angle A\) and \(\angle B\). The sum of adjacent angles with perpendicular exterior sides is \(90^\circ\) (since the lines are perpendicular, forming a right angle).
3. Recall the definition of complementary angles: Angles whose sum is \(90^\circ\) are complementary.
4. Eliminate other options:

• Supplementary angles sum to \(180^\circ\), so A is incorrect.
• Congruent angles have the same measure, but this isn't guaranteed here, so B is incorrect.
• The angles don't have to be right angles themselves (they just sum to \(90^\circ\)), so C is incorrect.
• Obtuse angles are greater than \(90^\circ\), so E is incorrect.

Answer:

D. complementary