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In the triangle above what is the measure of angle CDB?

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Source: — Data Sufficiency |

swerve wrote:Image

In the triangle above what is the measure of angle CDB?

1. Angle CAB = angle ACB = 30°.
2. AB = BC = BD.
Source: e-GMAT
$$? = \angle CDB = x$$
(All angles are measured in degrees.)

(1) Using the exterior angle property (to justify 30+30 in red), triangle BCD is equilateral (hence x=60). Sufficient!

(2) The constructions shown below are viable and present two different possible values for x. Insufficient!


Image

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
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