1988 AMC 8 Problem 5

Attempt Problem 5 of the 1988 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1988 AMC 8 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

5.

If ∠CBD\angle CBD is a right angle, then this protractor indicates that the measure of ∠ABC\angle ABC is approximately
20∘20^\circ
40∘40^\circ
50∘50^\circ
70∘70^\circ
120∘120^\circ
Answer: C
Concepts:angle chasing
Small hint:
On the protractor, ray BABA reads about 20∘20^\circ and ray BDBD reads about 160∘160^\circ
Big hint:
Since ∠CBD=90∘\angle CBD = 90^\circ and BDBD reads 160∘,160^\circ, ray BCBC reads 160∘−90∘.160^\circ - 90^\circ. Then ∠ABC\angle ABC is the difference between the readings of BCBC and BA.BA.
Solution:
Reading the protractor, ray BABA is at about 20∘20^\circ and ray BDBD is at about 160∘.160^\circ.
Because ∠CBD\angle CBD is a right angle, ray BCBC is at 160∘−90∘=70∘.160^\circ - 90^\circ = 70^\circ.
Therefore ∠ABC=70∘−20∘=50∘.\angle ABC = 70^\circ - 20^\circ = 50^\circ.
Thus, the correct answer is C .
LIVE by Po-Shen Loh
Programs

LIVE Classes

Self-Paced Classes

Stars

Scholarship

About Us

Who Is Po-Shen Loh?

Email Contact

Newsletter

Jobs

Become a Star

For a more Thought Full world.

© 2026 Expii, Inc.