2002 AMC 12A Problem 4

Below is the professionally curated solution for Problem 4 of the 2002 AMC 12A, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2002 AMC 12A solutions, or check the answer key.

All of the real AMC 8, AMC 10, AMC 12, and AIME problems in our complete solution collection are used with official legal permission of the Mathematical Association of America (MAA).

Concepts:angle sumlinear equation

Difficulty rating: 1130

4.

Find the degree measure of an angle whose complement is 25%25\% of its supplement.

4848

6060

7575

120120

150150

Solution:

Let the angle be x.x. Then 90x=14(180x),90 - x = \dfrac14(180 - x), so 3604x=180x.360 - 4x = 180 - x.

This gives 3x=180,3x = 180, so x=60.x = 60.

Thus, the correct answer is B.

Problem 4 in Other Years