Question

The measure of angle $ABC$ is $50^\circ$ . $\overline{AD}$ bisects angle $BAC$ , and $\overline{DC}$ bisects angle $BCA$ . The measure of angle $ADC$ is

$90^\circ$

$100^\circ$

$115^\circ$

$122.5^\circ$

$125^\circ$

Answer: C

Concepts:angle chasing angle bisector

Difficulty rating: 1150

Solution:

In triangle $ABC$ , $\angle BAC + \angle BCA = 180^\circ - 50^\circ$ $= 130^\circ$ .

The bisectors give $\angle DAC + \angle DCA = \tfrac{130^\circ}{2} = 65^\circ$ . In triangle $ADC$ , $\angle ADC = 180^\circ - 65^\circ = 115^\circ$ .

Thus, the correct answer is C .

1996 AMC 8 Problem 24

Answer: C

Difficulty rating: 1150

Solution:

Problem 24 in Other Years