Answer:
120°
Explanation:
You want to know the measure of the obtuse angle x° at B in the attached diagram.
Special triangles
This problem is quickly solved by using your knowledge of "special" triangles. Referring to the attached figure, triangles ACE and DGC are isosceles right triangles, so their base angles are 45°. Triangle CDE is equilateral, so all of its internal angles are 60°.
Straight angle
Line AB forms a "straight angle" at C. That means the sum of angles on one side of the line is 180°. This can be used to find the measure of angle DCB.
∠ACE +∠ECD +∠DCB = 180°
45° +60° +∠DCB = 180°
∠DCB = 180° -105° = 75°
From above, you know that angle CDG is 45°.
Remote interior angles
The marked angle x° is an exterior angle to triangle BCD. As such, its measure is equal to the sum of the remote interior angles of that triangle:
x° = ∠BCD +∠BDC = 75° +45°
x° = 120°
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Additional comment
As with many math problems there are other ways to work this. If you draw a perpendicular to AB at C, you find it makes a 45° angle with CE and a 15° angle with CD. That same 15° measure is the measure of angle GCB. Of course, angle G is 45°, so it takes x° = 120° to make the internal angle sum of ∆GCB equal to 180°.