MathDB

The measure of angle

ABC

50^\circ

\overline{AD}

bisects angle

BAC

, and

\overline{DC}

bisects angle

BCA

. The measure of angle

ADC

is
[asy] pair A,B,C,D; A = (0,0); B = (9,10); C = (10,0); D = (6.66,3); dot(A); dot(B); dot(C); dot(D); draw(A--B--C--cycle); draw(A--D--C);
label("

A

",A,SW); label("

B

",B,N); label("

C

",C,SE); label("

D

",D,N); label("

50^\circ

",(9.4,8.8),SW); [/asy]

\text{(A)}\ 90^\circ \qquad \text{(B)}\ 100^\circ \qquad \text{(C)}\ 115^\circ \qquad \text{(D)}\ 122.5^\circ \qquad \text{(E)}\ 125^\circ

Problem Statement