Measure of angle x

[beat_gmat_09]

In the figure to the right, point D divides side BC of triangle ABC into segments BD and DC of lengths 1 and 2 units respectively. Given that Angle ADC = 60 and Angle ABD = 45, what is the measure of angle x? (Note: Figure is not drawn to scale.)

(A) 55
(B) 60
(C) 70
(D) 75
(E) 90

[goyalsau]

I think it should be E,

Angle ADC is the exterior angle of Traingle ADC,

Angle BAD is 15,

as the segment AD divides the line CB in the ratio of 1:2,

Angle BAD, must be half of Angle CAD,

by this relation, Angle DAC is 30 ,

we have two angles of a triangle so angle C must be 90,

[beat_gmat_09]

I think it should be E,

Angle ADC is the exterior angle of Traingle ADC,

Angle BAD is 15,

as the segment AD divides the line CB in the ratio of 1:2,

Angle BAD, must be half of Angle CAD,

by this relation, Angle DAC is 30 ,

we have two angles of a triangle so angle C must be 90,

E is incorrect.

[goyalsau]

I think it should be E,

Angle ADC is the exterior angle of Traingle ADC,

Angle BAD is 15,

as the segment AD divides the line CB in the ratio of 1:2,

Angle BAD, must be half of Angle CAD,

by this relation, Angle DAC is 30 ,

we have two angles of a triangle so angle C must be 90,

E is incorrect.

What is the OA,
Do you have the explanation...
IF you have please post it then,

[beat_gmat_09]

I think it should be E,

Angle ADC is the exterior angle of Traingle ADC,

Angle BAD is 15,

as the segment AD divides the line CB in the ratio of 1:2,

Angle BAD, must be half of Angle CAD,

by this relation, Angle DAC is 30 ,

we have two angles of a triangle so angle C must be 90,

E is incorrect.

What is the OA,
Do you have the explanation...
IF you have please post it then,

OA is D. I dont have explanation.

[GMATGuruNY]

In the figure to the right, point D divides side BC of triangle ABC into segments BD and DC of lengths 1 and 2 units respectively. Given that Angle ADC = 60 and Angle ABD = 45, what is the measure of angle x? (Note: Figure is not drawn to scale.)

(A) 55
(B) 60
(C) 70
(D) 75
(E) 90

This is a very hard problem to solve without using trigonometry. The trick is to draw a 30:60:90 triangle and notice all the isosceles triangles that are created.

For one possible solution, please see the attachment.