Question

use the diagram to the right for questions 9 - 12: 13. name a pair of complementary angles:__________ 14. identify all angles that are congruent to ∠wyv:________ 15. name all angles that are supplementary to ∠xyv:________ 16. name all angles that form a linear pair with ∠wyv:__________

Explanation:

Step1: Recall angle - pair definitions

Complementary angles add up to 90 degrees, congruent angles have equal measures, supplementary angles add up to 180 degrees, and linear - pair angles are adjacent and add up to 180 degrees.

Step2: Find complementary angles

If there is a right - angle formed at the center (assume ∠XYT = 90°), then a pair of complementary angles could be ∠XYW and ∠WYT.

Step3: Identify congruent angles to ∠WYV

Vertical angles are congruent. If ∠WYV is given, its vertical angle ∠UYS is congruent to it. Also, if there are parallel lines and transversals creating corresponding or alternate angles (not shown clearly in the basic diagram but in a more complex scenario), other angles could be congruent. But just considering vertical angles, ∠UYS is congruent to ∠WYV.

Step4: Find supplementary angles to ∠XYV

Supplementary angles to ∠XYV are those that, when added to ∠XYV, equal 180 degrees. If we consider the straight - line formed by some rays, angles like ∠XYU (assuming a straight - line through Y) are supplementary to ∠XYV.

Step5: Find linear - pair angles to ∠WYV

Linear - pair angles to ∠WYV are adjacent angles that form a straight - line with it. For example, ∠WYV and ∠VYS form a linear pair.

Answer:

1. ∠XYW and ∠WYT
2. ∠UYS
3. ∠XYU
4. ∠VYS