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geometry intermediate

Problem

△ A B C

has a right angle at

C

and

∠ A = 2 0^{\circ}

. If

B D

(

D

in

\overline{A C}

) is the bisector of

∠ A B C

, then

∠ B D C =

(A)

4 0^{\circ}

(B)

4 5^{\circ}

(C)

5 0^{\circ}

(D)

5 5^{\circ}

Solution

Since

∠ C = 9 0^{\circ}

and

∠ A = 2 0^{\circ}

, we have

∠ A B C = 7 0^{\circ}

. Thus

∠ D B C = 3 5^{\circ}

. It follows that

∠ B D C = 9 0^{\circ} - 3 5^{\circ} = 5 5^{\circ}

, which is

5 5^{\circ}

.

Final answer

D