1996 AMC 8 Problem 24

Attempt Problem 24 of the 1996 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 1996 AMC 8 solutions, or check the answer key.

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

24.

The measure of angle ABCABC is 50∘.50^\circ. AD‾\overline{AD} bisects angle BAC,BAC, and DC‾\overline{DC} bisects angle BCA.BCA. The measure of angle ADCADC is
90∘90^\circ
100∘100^\circ
115∘115^\circ
122.5∘122.5^\circ
125∘125^\circ
Answer: C
Concepts:angle chasingangle bisector
Small hint:
In triangle ABC,ABC, angles BACBAC and BCABCA add to 180∘−50∘=130∘180^\circ - 50^\circ = 130^\circ
Big hint:
The bisected halves at AA and CC add to 65∘;65^\circ; use the angle sum in triangle ADCADC
Solution:
In triangle ABC,ABC, ∠BAC+∠BCA=180∘−50∘=130∘. \begin{aligned} \angle BAC + \angle BCA &= 180^\circ - 50^\circ \\ &= 130^\circ. \end{aligned}
The bisectors give ∠DAC+∠DCA=130∘2=65∘.\angle DAC + \angle DCA = \tfrac{130^\circ}{2} = 65^\circ. In triangle ADC,ADC, ∠ADC=180∘−65∘=115∘.\angle ADC = 180^\circ - 65^\circ = 115^\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.