In triangle ABC, DB and DC are angle bisectors and the angle BAC = 60°

Question

Tough and Tricky questions: Geometry. https://gmatclub.com/forum/download/file.php?id=25227 In triangle ABC, DB and DC are angle bisectors and the angle BAC = 60°. If angle DCB is 40°, what is the degree measure of angle DBC? (Note: Figure not drawn to scale.) A. 40° B. 35° C. 25° D. 20° E. 15° Kudos for a correct solution . 2015-01-06_1915.png

aeropower · Answer

Since DB and DC are angle bisectors, they cut the other angle into two equal parts.

Since DCB = 40 degrees; ACB = 80 degrees

Triangle degrees = BAC degrees + ACB degrees + ABC degrees
180 = 60 (given) + 80 + ABC degrees
40 degrees = ABC

Since DB bisects ABC = 40/20 = 20

Answer is D - 20 degrees

akmahajan89 · Answer

DC is the angle bisector for ACB
As DCB= 40,
ACB=80

Now sum of all angles=180

Therefore

ABC=180-(80+60)
ABC=40

Thus as BD is the angle bisector

DBC=20

Answer: D

g106 · Answer

Angle DCB = 40°
ACB = 2*DCB = 80°
ABC+ACB+BAC = 180°
ABC = 40°

DBC = ABC / 2 = 40°/2 = 20°

Ans D

PareshGmat · Answer

Answer = D = 20 Refer diagram below: 2015-01-06_1915.png

DesiGmat · Answer

Property of Angular Bisectors =

Angle BDC = 90 + 1/2(Angle BAC) = 90 + 30 = 120

So DBC = 180 - 120 - 40(given) = 20

Option D

Bunuel · Answer

OFFICIAL SOLUTION:

(D) First of all remember that the sum of all angles in a triangle is equal to 180°. We are told that angle BAC = 60°. That leaves 120° to be split between angles ABC and ACB. We know that DC and DB are angle bisectors (an angle bisector can be described as a line segment that divides an angle into two equal angles), AND we are told that angle DCB is 40°. Therefore we can find the value of angle ACB by doubling DCB, i.e. 40° × 2 = 80°. Now we have the values of two of the angles in triangle ABC: 60° + 80° = 140°, leaving 40° for angle ABC. Knowing that DB splits angle ABC in half, all we have to do is to divide 40° by 2 and we get the answer. The value for DBC is 40° / 2 = 20°.

The correct answer is D.

KanishkM · Answer

Here are my two cents

Since DB and DC are angle bisectors, < BAC = 60° and If angle DCB is 40° then < ACB will be = 80°

As an angle bisector divides an angle in 2 equal parts.

Then consider the Triangle ABC, < ABC + < ACB + <BAC = 180°
This will give <ABC = 40°

As DB is an angle bisector, <DBC = 20°, Giving the correct answer as D

Correct Answer  D .

bumpbot · Answer

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In triangle ABC, DB and DC are angle bisectors and the angle BAC = 60°

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In triangle ABC, DB and DC are angle bisectors and the angle BAC = 60°

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