In the figure, △ ABC has a right angle at C and ∠ A=20°. If BD is the bisector of ∠ ABC, then ∠ BDC=

1986 AMC 12 Problem 3

Attempt Problem 3 of the 1986 AMC 12 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 1986 AMC 12 solutions, or check the answer key.

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

In the figure,

\triangle ABC

has a right angle at

C

and

\angle A=20^\circ.

BD

is the bisector of

\angle ABC,

then

\angle BDC=

40^\circ

45^\circ

50^\circ

55^\circ

60^\circ

First find

\angle ABC

from the angle sum of

\triangle ABC

Use the bisector and then the angle sum of right triangle

BDC

Since

\angle C=90^\circ

and

\angle A=20^\circ,

we have

\angle ABC=70^\circ.

The bisector gives

\angle DBC=35^\circ.

Therefore, in right triangle

BDC,

\angle BDC=90^\circ-35^\circ=55^\circ.

Thus the correct answer is D.