Question

question 9 (4 points)
a stair railing is designed as shown in the figure.
match the type of angles with the angles identified in the figure.
column a

1. complementary angles
2. supplementary angles
3. vertical angles
4. adjacent angles

column b
a. ∠8&∠5
b. ∠1&∠2
c. ∠1&∠2
d. ∠7&∠5
e. ∠8&∠2

Explanation:

Step1: Recall angle - pair definitions

Complementary angles add up to 90 degrees. Supplementary angles add up to 180 degrees. Vertical angles are opposite each other when two lines intersect. Adjacent angles share a common side and a common vertex.

Step2: Analyze complementary angles

In the figure, if we assume right - angled corners, \(\angle1\) and \(\angle2\) can form a right - angle (90 degrees), so they are complementary angles.

Step3: Analyze supplementary angles

There are no two angles in the given options that clearly add up to 180 degrees. But if we consider the linear pairs in a more general sense, we can assume non - given linear pairs. However, based on the options, there is no correct supplementary - angle pair.

Step4: Analyze vertical angles

\(\angle8\) and \(\angle5\) are vertical angles as they are opposite each other when two lines intersect.

Step5: Analyze adjacent angles

\(\angle7\) and \(\angle5\) share a common side and a common vertex, so they are adjacent angles.

Answer:

1. b. \(\angle1\&\angle2\)
2. None of the above (no correct option in the given list for supplementary angles)
3. a. \(\angle8\&\angle5\)
4. d. \(\angle7\&\angle5\)